# Berlekamp Massey Algorithm

I am trying to solve the BM algorithm to find the shortest LFSR and the feedback polynomial but i keep getting stuck. Is there anybody who could solve any binary code so the steps could be little clear. I had seen the algorithm on Wikepedia but too many letters without any implemented examples are very confusing for me. I would be very grateful if someone could explain the steps with actual numbers. Any numerical example would work.

• The code there is short and works. It is only marginally less ugly than what it started from, which is a tentative implementation of Wikipedia pseudocode. I wish I had time to make a clear/clean version in python. But there's little hope for the next 5 days.
– fgrieu
Commented Jan 30, 2019 at 9:00
• i pretty much understood alot from the code but i still want to be able to do everything by hand and not by using the code. So i was trying to figure out this part. Commented Jan 30, 2019 at 9:46
• s[ 0] := 1 s[ 1] := 1 s[ 2] := 0 s[ 3] := 0 s[ 4] := 0 s[ 5] := s[ 3] ^ s[ 1] ^ s[ 0] = 0 ^ 1 ^ 1 = 0 s[ 6] := s[ 4] ^ s[ 2] ^ s[ 1] = 0 ^ 0 ^ 1 = 1 s[ 7] := s[ 5] ^ s[ 3] ^ s[ 2] = 0 ^ 0 ^ 0 = 0 s[ 8] := s[ 6] ^ s[ 4] ^ s[ 3] = 1 ^ 0 ^ 0 = 1 s[ 9] := s[ 7] ^ s[ 5] ^ s[ 4] = 0 ^ 0 ^ 0 = 0 s[10] := s[ 8] ^ s[ 6] ^ s[ 5] = 1 ^ 1 ^ 0 = 0 s[11] := s[ 9] ^ s[ 7] ^ s[ 6] = 0 ^ 0 ^ 1 = 1 Commented Jan 30, 2019 at 9:47
• is it possible if u could explain this in a little detail that why did u start with s[5] and how did u get s[0] s[1] and s[3] in the s[5] part? Commented Jan 30, 2019 at 9:48
• What you quote is code/expressions that apply the recurrence $s_{i+5}←s_{i+3}⊕s_{i+1}⊕s_i$, found by the BM code (in C) at the end of the linked post. That recurrence defines a Fibonnaci LFSR. The first 5 $s_i$ are the first 5 values at the input of BM, here {1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1}. The next $s_i$ are computed per the recurrence, and match the next values at input of BM, because that's what BM is about.
– fgrieu
Commented Jan 30, 2019 at 10:11

This is a Testing of Berlekamp Massey

Input =This is a Testing of Berlekamp Massey Input =01010100011010000110100101110011001000000110100101110011001000000110000100100000010101000110010101110011011101000110100101101110011001110010000001101111011001100010000001000010011001010111001001101100011001010110101101100001011011010111000000100000010011010110000101110011011100110110010101111001 Long =296 Bit

GF2 Binary=1null d=0 T= C= 1 l= 0 m= -1 b= 1 N= 1 d=1 T= 1 C= 1+x2 l= 2 m= 1 b= 1 N= 2 d=0 T= 1 C= 1+x2 l= 2 m= 1 b= 1 N= 3 d=0 T= 1 C= 1+x2 l= 2 m= 1 b= 1 N= 4 d=0 T= 1 C= 1+x2 l= 2 m= 1 b= 1 N= 5 d=0 T= 1 C= 1+x2 l= 2 m= 1 b= 1 N= 6 d=0 T= 1 C= 1+x2 l= 2 m= 1 b= 1 N= 7 d=1 T= 1+x2 C= 1+x2+x6 l= 6 m= 7 b= 1+x2 N= 8 d=0 T= 1+x2 C= 1+x2+x6 l= 6 m= 7 b= 1+x2 N= 9 d=0 T= 1+x2 C= 1+x2+x6 l= 6 m= 7 b= 1+x2 N= 10 d=1 T= 1+x2+x6 C= 1+x2+x3+x5+x6 l= 6 m= 7 b= 1+x2 N= 11 d=0 T= 1+x2+x6 C= 1+x2+x3+x5+x6 l= 6 m= 7 b= 1+x2 N= 12 d=1 T= 1+x2+x3+x5+x6 C= 1+x2+x3+x6+x7 l= 7 m= 12 b= 1+x2+x3+x5+x6 N= 13 ...shortly... d=0 T= 1+x1+x3+x4+x5+x9+x11+x13+x16+x18+x19+x21+x22+x23+x29+x33+x35+x36+x39+x41+x42+x43+x47+x48+x50+x51+x53+x55+x56+x62+x63+x64+x66+x67+x71+x75+x79+x81+x82+x83+x85+x86+x87+x90+x92+x94+x95+x96+x99+x100+x103+x107+x108+x109+x112+x113+x117+x119+x120+x121+x122+x123+x125+x127+x128+x130+x135+x141+x142+x143+x145 C= 1+x1+x2+x3+x7+x8+x13+x14+x16+x17+x20+x21+x23+x24+x25+x26+x31+x34+x40+x41+x45+x47+x48+x52+x53+x54+x55+x56+x59+x61+x62+x65+x69+x70+x75+x76+x78+x81+x82+x84+x88+x92+x93+x94+x96+x98+x100+x102+x104+x105+x106+x107+x108+x109+x111+x112+x113+x116+x117+x119+x122+x123+x124+x125+x126+x127+x132+x134+x139+x141+x143+x144+x146 l= 146 m= 290 b= 1+x1+x3+x4+x5+x9+x11+x13+x16+x18+x19+x21+x22+x23+x29+x33+x35+x36+x39+x41+x42+x43+x47+x48+x50+x51+x53+x55+x56+x62+x63+x64+x66+x67+x71+x75+x79+x81+x82+x83+x85+x86+x87+x90+x92+x94+x95+x96+x99+x100+x103+x107+x108+x109+x112+x113+x117+x119+x120+x121+x122+x123+x125+x127+x128+x130+x135+x141+x142+x143+x145 N= 292 d=0 T= 1+x1+x3+x4+x5+x9+x11+x13+x16+x18+x19+x21+x22+x23+x29+x33+x35+x36+x39+x41+x42+x43+x47+x48+x50+x51+x53+x55+x56+x62+x63+x64+x66+x67+x71+x75+x79+x81+x82+x83+x85+x86+x87+x90+x92+x94+x95+x96+x99+x100+x103+x107+x108+x109+x112+x113+x117+x119+x120+x121+x122+x123+x125+x127+x128+x130+x135+x141+x142+x143+x145 C= 1+x1+x2+x3+x7+x8+x13+x14+x16+x17+x20+x21+x23+x24+x25+x26+x31+x34+x40+x41+x45+x47+x48+x52+x53+x54+x55+x56+x59+x61+x62+x65+x69+x70+x75+x76+x78+x81+x82+x84+x88+x92+x93+x94+x96+x98+x100+x102+x104+x105+x106+x107+x108+x109+x111+x112+x113+x116+x117+x119+x122+x123+x124+x125+x126+x127+x132+x134+x139+x141+x143+x144+x146 l= 146 m= 290 b= 1+x1+x3+x4+x5+x9+x11+x13+x16+x18+x19+x21+x22+x23+x29+x33+x35+x36+x39+x41+x42+x43+x47+x48+x50+x51+x53+x55+x56+x62+x63+x64+x66+x67+x71+x75+x79+x81+x82+x83+x85+x86+x87+x90+x92+x94+x95+x96+x99+x100+x103+x107+x108+x109+x112+x113+x117+x119+x120+x121+x122+x123+x125+x127+x128+x130+x135+x141+x142+x143+x145 N= 293 d=1 T= 1+x1+x2+x3+x7+x8+x13+x14+x16+x17+x20+x21+x23+x24+x25+x26+x31+x34+x40+x41+x45+x47+x48+x52+x53+x54+x55+x56+x59+x61+x62+x65+x69+x70+x75+x76+x78+x81+x82+x84+x88+x92+x93+x94+x96+x98+x100+x102+x104+x105+x106+x107+x108+x109+x111+x112+x113+x116+x117+x119+x122+x123+x124+x125+x126+x127+x132+x134+x139+x141+x143+x144+x146 C= 1+x1+x2+x4+x6+x12+x13+x17+x19+x20+x22+x23+x31+x32+x34+x36+x38+x39+x40+x41+x42+x44+x46+x47+x48+x50+x51+x52+x55+x58+x61+x62+x66+x67+x74+x75+x76+x81+x85+x86+x89+x90+x92+x94+x95+x96+x97+x99+x100+x103+x104+x105+x107+x108+x109+x110+x113+x115+x117+x119+x120+x127+x128+x130+x131+x132+x133+x134+x138+x139+x141+x143+x145+x148 l= 148 m= 293 b= 1+x1+x2+x3+x7+x8+x13+x14+x16+x17+x20+x21+x23+x24+x25+x26+x31+x34+x40+x41+x45+x47+x48+x52+x53+x54+x55+x56+x59+x61+x62+x65+x69+x70+x75+x76+x78+x81+x82+x84+x88+x92+x93+x94+x96+x98+x100+x102+x104+x105+x106+x107+x108+x109+x111+x112+x113+x116+x117+x119+x122+x123+x124+x125+x126+x127+x132+x134+x139+x141+x143+x144+x146 N= 294 d=1 T= 1+x1+x2+x4+x6+x12+x13+x17+x19+x20+x22+x23+x31+x32+x34+x36+x38+x39+x40+x41+x42+x44+x46+x47+x48+x50+x51+x52+x55+x58+x61+x62+x66+x67+x74+x75+x76+x81+x85+x86+x89+x90+x92+x94+x95+x96+x97+x99+x100+x103+x104+x105+x107+x108+x109+x110+x113+x115+x117+x119+x120+x127+x128+x130+x131+x132+x133+x134+x138+x139+x141+x143+x145+x148 C= 1+x3+x6+x8+x9+x12+x13+x14+x15+x18+x19+x20+x21+x23+x24+x25+x26+x27+x31+x34+x35+x36+x38+x39+x40+x44+x47+x49+x50+x51+x52+x53+x54+x56+x57+x58+x60+x61+x63+x67+x70+x71+x74+x75+x77+x79+x81+x82+x83+x86+x90+x92+x93+x96+x100+x101+x104+x106+x112+x114+x115+x118+x119+x123+x124+x125+x126+x130+x131+x132+x134+x135+x138+x139+x140+x141+x142+x143+x144+x147+x148 l= 148 m= 293 b= 1+x1+x2+x3+x7+x8+x13+x14+x16+x17+x20+x21+x23+x24+x25+x26+x31+x34+x40+x41+x45+x47+x48+x52+x53+x54+x55+x56+x59+x61+x62+x65+x69+x70+x75+x76+x78+x81+x82+x84+x88+x92+x93+x94+x96+x98+x100+x102+x104+x105+x106+x107+x108+x109+x111+x112+x113+x116+x117+x119+x122+x123+x124+x125+x126+x127+x132+x134+x139+x141+x143+x144+x146 N= 295 d=1 T= 1+x3+x6+x8+x9+x12+x13+x14+x15+x18+x19+x20+x21+x23+x24+x25+x26+x27+x31+x34+x35+x36+x38+x39+x40+x44+x47+x49+x50+x51+x52+x53+x54+x56+x57+x58+x60+x61+x63+x67+x70+x71+x74+x75+x77+x79+x81+x82+x83+x86+x90+x92+x93+x96+x100+x101+x104+x106+x112+x114+x115+x118+x119+x123+x124+x125+x126+x130+x131+x132+x134+x135+x138+x139+x140+x141+x142+x143+x144+x147+x148 C= 1+x2+x4+x5+x6+x8+x10+x12+x13+x14+x16+x20+x21+x22+x24+x28+x31+x33+x34+x35+x38+x39+x40+x42+x43+x44+x51+x52+x53+x55+x60+x64+x70+x72+x74+x75+x78+x79+x80+x81+x82+x84+x92+x93+x94+x95+x98+x101+x102+x107+x108+x109+x110+x111+x112+x113+x121+x123+x127+x128+x129+x130+x131+x132+x135+x136+x138+x139+x140+x142+x144+x145+x146+x147 l= 148 m= 293 b= 1+x1+x2+x3+x7+x8+x13+x14+x16+x17+x20+x21+x23+x24+x25+x26+x31+x34+x40+x41+x45+x47+x48+x52+x53+x54+x55+x56+x59+x61+x62+x65+x69+x70+x75+x76+x78+x81+x82+x84+x88+x92+x93+x94+x96+x98+x100+x102+x104+x105+x106+x107+x108+x109+x111+x112+x113+x116+x117+x119+x122+x123+x124+x125+x126+x127+x132+x134+x139+x141+x143+x144+x146 N= 296

Input =01010100011010000110100101110011001000000110100101110011001000000110000100100000010101000110010101110011011101000110100101101110011001110010000001101111011001100010000001000010011001010111001001101100011001010110101101100001011011010111000000100000010011010110000101110011011100110110010101111001 Init ( To get init was came from backward of Input with length of maximum degree of polynomial) =0110000001001110011001110110100101100010111011001110101001100010101000000100100001100000010011001110100101100000010011001110100101100001011000101010

Poly =1010111010101110100011101000100101110011101110000001110100001000100000101011001111101000000011110010011000011111110000000101000111111001101110101111 Polinomial=1+x2+x4+x5+x6+x8+x10+x12+x13+x14+x16+x20+x21+x22+x24+x28+x31+x33+x34+x35+x38+x39+x40+x42+x43+x44+x51+x52+x53+x55+x60+x64+x70+x72+x74+x75+x78+x79+x80+x81+x82+x84+x92+x93+x94+x95+x98+x101+x102+x107+x108+x109+x110+x111+x112+x113+x121+x123+x127+x128+x129+x130+x131+x132+x135+x136+x138+x139+x140+x142+x144+x145+x146+x147

LFSR Process :

Generate Process... Mesin=1010111010101110100011101000100101110011101110000001110100001000100000101011001111101000000011110010011000011111110000000101000111111001101110101111 Init =0110000001001110011001110110100101100010111011001110101001100010101000000100100001100000010011001110100101100000010011001110100101100001011000101010 Register=1011000000100111001100111011010010110001011101100111010100110001010100000010010000110000001001100111010010110000001001100111010010110000101100010101 Out=0 feedback no=1 Register=1101100000010011100110011101101001011000101110110011101010011000101010000001001000011000000100110011101001011000000100110011101001011000010110001010 Out=1 feedback no=2 Register=1110110000001001110011001110110100101100010111011001110101001100010101000000100100001100000010011001110100101100000010011001110100101100001011000101 Out=0 feedback no=3 ...shortly Register=0010100001101011101101000111111100000111011010001000010111100101100000100011110101111111100101100110100000101100000011010100110011001001100110101101 Out=0 feedback no=295 Register=1001010000110101110110100011111110000011101101000100001011110010110000010001111010111111110010110011010000010110000001101010011001100100110011010110 Out=1 feedback no=296

Result: 01010100011010000110100101110011001000000110100101110011001000000110000100100000010101000110010101110011011101000110100101101110011001110010000001101111011001100010000001000010011001010111001001101100011001010110101101100001011011010111000000100000010011010110000101110011011100110110010101111001 "This is a Testing of Berlekamp Massey"

Inputan proses Barlekamp Massey teks=Short Test null d=0 T= C= 1 l= 0 m= -1 b= 1 N= 1 d=1 T= 1 C= 1+x2 l= 2 m= 1 b= 1 N= 2 d=0 T= 1 C= 1+x2 l= 2 m= 1 b= 1 N= 3 d=0 T= 1 C= 1+x2 l= 2 m= 1 b= 1 N= 4 d=0 T= 1 C= 1+x2 l= 2 m= 1 b= 1 N= 5 d=1 T= 1+x2 C= 1+x2+x4 l= 4 m= 5 b= 1+x2 N= 6 d=1 T= 1+x2+x4 C= 1+x1+x2+x3+x4 l= 4 m= 5 b= 1+x2 N= 7 d=1 T= 1+x1+x2+x3+x4 C= 1+x1+x3 l= 4 m= 5 b= 1+x2 N= 8 d=1 T= 1+x1+x3 C= 1+x1+x5 l= 5 m= 8 b= 1+x1+x3 N= 9 d=1 T= 1+x1+x5 C= 1+x2+x4+x5 l= 5 m= 8 b= 1+x1+x3 N= 10 d=0 T= 1+x1+x5 C= 1+x2+x4+x5 l= 5 m= 8 b= 1+x1+x3 N= 11 d=1 T= 1+x2+x4+x5 C= 1+x2+x3+x5+x6 l= 7 m= 11 b= 1+x2+x4+x5 N= 12 d=1 T= 1+x2+x3+x5+x6 C= 1+x1+x2 l= 7 m= 11 b= 1+x2+x4+x5 N= 13 d=1 T= 1+x1+x2 C= 1+x1+x4+x6+x7 l= 7 m= 11 b= 1+x2+x4+x5 N= 14 d=0 T= 1+x1+x2 C= 1+x1+x4+x6+x7 l= 7 m= 11 b= 1+x2+x4+x5 N= 15 d=1 T= 1+x1+x4+x6+x7 C= 1+x1+x7+x8+x9 l= 9 m= 15 b= 1+x1+x4+x6+x7 N= 16 d=0 T= 1+x1+x4+x6+x7 C= 1+x1+x7+x8+x9 l= 9 m= 15 b= 1+x1+x4+x6+x7 N= 17 d=1 T= 1+x1+x7+x8+x9 C= 1+x1+x2+x3+x6+x7 l= 9 m= 15 b= 1+x1+x4+x6+x7 N= 18 d=1 T= 1+x1+x2+x3+x6+x7 C= 1+x1+x2+x4+x6+x9+x10 l= 10 m= 18 b= 1+x1+x2+x3+x6+x7 N= 19 d=0 T= 1+x1+x2+x3+x6+x7 C= 1+x1+x2+x4+x6+x9+x10 l= 10 m= 18 b= 1+x1+x2+x3+x6+x7 N= 20 d=1 T= 1+x1+x2+x4+x6+x9+x10 C= 1+x1+x3+x5+x6+x8+x10 l= 11 m= 20 b= 1+x1+x2+x4+x6+x9+x10 N= 21 d=1 T= 1+x1+x3+x5+x6+x8+x10 C= 1+x2+x6+x7+x8+x11 l= 11 m= 20 b= 1+x1+x2+x4+x6+x9+x10 N= 22 d=0 T= 1+x1+x3+x5+x6+x8+x10 C= 1+x2+x6+x7+x8+x11 l= 11 m= 20 b= 1+x1+x2+x4+x6+x9+x10 N= 23 d=0 T= 1+x1+x3+x5+x6+x8+x10 C= 1+x2+x6+x7+x8+x11 l= 11 m= 20 b= 1+x1+x2+x4+x6+x9+x10 N= 24 d=1 T= 1+x2+x6+x7+x8+x11 C= 1+x2+x4+x5+x7+x10+x11+x13+x14 l= 14 m= 24 b= 1+x2+x6+x7+x8+x11 N= 25 d=0 T= 1+x2+x6+x7+x8+x11 C= 1+x2+x4+x5+x7+x10+x11+x13+x14 l= 14 m= 24 b= 1+x2+x6+x7+x8+x11 N= 26 d=0 T= 1+x2+x6+x7+x8+x11 C= 1+x2+x4+x5+x7+x10+x11+x13+x14 l= 14 m= 24 b= 1+x2+x6+x7+x8+x11 N= 27 d=0 T= 1+x2+x6+x7+x8+x11 C= 1+x2+x4+x5+x7+x10+x11+x13+x14 l= 14 m= 24 b= 1+x2+x6+x7+x8+x11 N= 28 d=1 T= 1+x2+x4+x5+x7+x10+x11+x13+x14 C= 1+x2+x5+x6+x7+x12+x13+x14+x15 l= 15 m= 28 b= 1+x2+x4+x5+x7+x10+x11+x13+x14 N= 29 d=0 T= 1+x2+x4+x5+x7+x10+x11+x13+x14 C= 1+x2+x5+x6+x7+x12+x13+x14+x15 l= 15 m= 28 b= 1+x2+x4+x5+x7+x10+x11+x13+x14 N= 30 d=1 T= 1+x2+x5+x6+x7+x12+x13+x14+x15 C= 1+x4+x5+x9+x14+x16 l= 16 m= 30 b= 1+x2+x5+x6+x7+x12+x13+x14+x15 N= 31 d=0 T= 1+x2+x5+x6+x7+x12+x13+x14+x15 C= 1+x4+x5+x9+x14+x16 l= 16 m= 30 b= 1+x2+x5+x6+x7+x12+x13+x14+x15 N= 32 d=1 T= 1+x4+x5+x9+x14+x16 C= 1+x2+x5+x7+x8+x15+x17 l= 17 m= 32 b= 1+x4+x5+x9+x14+x16 N= 33 d=0 T= 1+x4+x5+x9+x14+x16 C= 1+x2+x5+x7+x8+x15+x17 l= 17 m= 32 b= 1+x4+x5+x9+x14+x16 N= 34 d=0 T= 1+x4+x5+x9+x14+x16 C= 1+x2+x5+x7+x8+x15+x17 l= 17 m= 32 b= 1+x4+x5+x9+x14+x16 N= 35 d=0 T= 1+x4+x5+x9+x14+x16 C= 1+x2+x5+x7+x8+x15+x17 l= 17 m= 32 b= 1+x4+x5+x9+x14+x16 N= 36 d=0 T= 1+x4+x5+x9+x14+x16 C= 1+x2+x5+x7+x8+x15+x17 l= 17 m= 32 b= 1+x4+x5+x9+x14+x16 N= 37 d=1 T= 1+x2+x5+x7+x8+x15+x17 C= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 l= 21 m= 37 b= 1+x2+x5+x7+x8+x15+x17 N= 38 d=0 T= 1+x2+x5+x7+x8+x15+x17 C= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 l= 21 m= 37 b= 1+x2+x5+x7+x8+x15+x17 N= 39 d=0 T= 1+x2+x5+x7+x8+x15+x17 C= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 l= 21 m= 37 b= 1+x2+x5+x7+x8+x15+x17 N= 40 d=0 T= 1+x2+x5+x7+x8+x15+x17 C= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 l= 21 m= 37 b= 1+x2+x5+x7+x8+x15+x17 N= 41 d=0 T= 1+x2+x5+x7+x8+x15+x17 C= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 l= 21 m= 37 b= 1+x2+x5+x7+x8+x15+x17 N= 42 d=0 T= 1+x2+x5+x7+x8+x15+x17 C= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 l= 21 m= 37 b= 1+x2+x5+x7+x8+x15+x17 N= 43 d=1 T= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 C= 1+x2+x6+x7+x9+x10+x11+x13+x15+x17+x19+x23 l= 23 m= 43 b= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 N= 44 d=0 T= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 C= 1+x2+x6+x7+x9+x10+x11+x13+x15+x17+x19+x23 l= 23 m= 43 b= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 N= 45 d=1 T= 1+x2+x6+x7+x9+x10+x11+x13+x15+x17+x19+x23 C= 1+x4+x6+x7+x12+x13+x15+x16+x21 l= 23 m= 43 b= 1+x2+x7+x8+x9+x10+x14+x15+x17+x19+x21 N= 46 d=1 T= 1+x4+x6+x7+x12+x13+x15+x16+x21 C= 1+x3+x4+x5+x6+x7+x10+x11+x15+x16+x17+x18+x20+x21+x22+x24 l= 24 m= 46 b= 1+x4+x6+x7+x12+x13+x15+x16+x21 N= 47 d=1 T= 1+x3+x4+x5+x6+x7+x10+x11+x15+x16+x17+x18+x20+x21+x22+x24 C= 1+x1+x3+x4+x6+x8+x10+x11+x13+x14+x15+x18+x20+x21+x24 l= 24 m= 46 b= 1+x4+x6+x7+x12+x13+x15+x16+x21 N= 48 d=1 T= 1+x1+x3+x4+x6+x8+x10+x11+x13+x14+x15+x18+x20+x21+x24 C= 1+x1+x2+x3+x4+x9+x10+x11+x13+x17+x20+x21+x23+x24 l= 25 m= 48 b= 1+x1+x3+x4+x6+x8+x10+x11+x13+x14+x15+x18+x20+x21+x24 N= 49 d=1 T= 1+x1+x2+x3+x4+x9+x10+x11+x13+x17+x20+x21+x23+x24 C= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 l= 25 m= 48 b= 1+x1+x3+x4+x6+x8+x10+x11+x13+x14+x15+x18+x20+x21+x24 N= 50 d=0 T= 1+x1+x2+x3+x4+x9+x10+x11+x13+x17+x20+x21+x23+x24 C= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 l= 25 m= 48 b= 1+x1+x3+x4+x6+x8+x10+x11+x13+x14+x15+x18+x20+x21+x24 N= 51 d=0 T= 1+x1+x2+x3+x4+x9+x10+x11+x13+x17+x20+x21+x23+x24 C= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 l= 25 m= 48 b= 1+x1+x3+x4+x6+x8+x10+x11+x13+x14+x15+x18+x20+x21+x24 N= 52 d=1 T= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 C= 1+x3+x4+x8+x13+x16+x18+x20+x23+x28 l= 28 m= 52 b= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 N= 53 d=1 T= 1+x3+x4+x8+x13+x16+x18+x20+x23+x28 C= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 l= 28 m= 52 b= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 N= 54 d=0 T= 1+x3+x4+x8+x13+x16+x18+x20+x23+x28 C= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 l= 28 m= 52 b= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 N= 55 d=0 T= 1+x3+x4+x8+x13+x16+x18+x20+x23+x28 C= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 l= 28 m= 52 b= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 N= 56 d=0 T= 1+x3+x4+x8+x13+x16+x18+x20+x23+x28 C= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 l= 28 m= 52 b= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 N= 57 d=0 T= 1+x3+x4+x8+x13+x16+x18+x20+x23+x28 C= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 l= 28 m= 52 b= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 N= 58 d=0 T= 1+x3+x4+x8+x13+x16+x18+x20+x23+x28 C= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 l= 28 m= 52 b= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 N= 59 d=0 T= 1+x3+x4+x8+x13+x16+x18+x20+x23+x28 C= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 l= 28 m= 52 b= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 N= 60 d=0 T= 1+x3+x4+x8+x13+x16+x18+x20+x23+x28 C= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 l= 28 m= 52 b= 1+x3+x5+x7+x10+x12+x13+x14+x15+x16+x17+x19+x20+x22+x23+x24+x25 N= 61 d=1 T= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 C= 1+x1+x3+x6+x9+x11+x12+x15+x16+x17+x19+x22+x23+x29+x31+x32+x33+x34 l= 34 m= 61 b= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 N= 62 d=1 T= 1+x1+x3+x6+x9+x11+x12+x15+x16+x17+x19+x22+x23+x29+x31+x32+x33+x34 C= 1+x2+x3+x4+x6+x7+x9+x11+x17+x18+x19+x23+x25+x26+x27+x31+x32+x33+x34 l= 34 m= 61 b= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 N= 63 d=1 T= 1+x2+x3+x4+x6+x7+x9+x11+x17+x18+x19+x23+x25+x26+x27+x31+x32+x33+x34 C= 1+x4+x5+x6+x7+x8+x9+x11+x13+x16+x18+x25+x28+x30+x31+x32+x33+x34 l= 34 m= 61 b= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 N= 64 d=1 T= 1+x4+x5+x6+x7+x8+x9+x11+x13+x16+x18+x25+x28+x30+x31+x32+x33+x34 C= 1+x3+x5+x7+x8+x11+x13+x14+x16+x17+x20+x24+x25+x27+x29+x30+x32+x33+x34 l= 34 m= 61 b= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 N= 65 d=1 T= 1+x3+x5+x7+x8+x11+x13+x14+x16+x17+x20+x24+x25+x27+x29+x30+x32+x33+x34 C= 1+x3+x4+x8+x10+x11+x13+x14+x15+x16+x17+x18+x19+x20+x21+x24+x27+x28+x33+x34 l= 34 m= 61 b= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 N= 66 d=0 T= 1+x3+x5+x7+x8+x11+x13+x14+x16+x17+x20+x24+x25+x27+x29+x30+x32+x33+x34 C= 1+x3+x4+x8+x10+x11+x13+x14+x15+x16+x17+x18+x19+x20+x21+x24+x27+x28+x33+x34 l= 34 m= 61 b= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 N= 67 d=0 T= 1+x3+x5+x7+x8+x11+x13+x14+x16+x17+x20+x24+x25+x27+x29+x30+x32+x33+x34 C= 1+x3+x4+x8+x10+x11+x13+x14+x15+x16+x17+x18+x19+x20+x21+x24+x27+x28+x33+x34 l= 34 m= 61 b= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 N= 68 d=0 T= 1+x3+x5+x7+x8+x11+x13+x14+x16+x17+x20+x24+x25+x27+x29+x30+x32+x33+x34 C= 1+x3+x4+x8+x10+x11+x13+x14+x15+x16+x17+x18+x19+x20+x21+x24+x27+x28+x33+x34 l= 34 m= 61 b= 1+x1+x3+x6+x11+x14+x15+x17+x21+x24+x25+x26+x28 N= 69 d=1 T= 1+x3+x4+x8+x10+x11+x13+x14+x15+x16+x17+x18+x19+x20+x21+x24+x27+x28+x33+x34 C= 1+x3+x4+x9+x10+x13+x15+x16+x17+x18+x20+x21+x22+x23+x24+x25+x27+x28+x29+x32+x36 l= 36 m= 69 b= 1+x3+x4+x8+x10+x11+x13+x14+x15+x16+x17+x18+x19+x20+x21+x24+x27+x28+x33+x34 N= 70 d=1 T= 1+x3+x4+x9+x10+x13+x15+x16+x17+x18+x20+x21+x22+x23+x24+x25+x27+x28+x29+x32+x36 C= 1+x1+x3+x5+x10+x11+x12+x13+x14+x19+x23+x24+x27+x32+x34+x35+x36 l= 36 m= 69 b= 1+x3+x4+x8+x10+x11+x13+x14+x15+x16+x17+x18+x19+x20+x21+x24+x27+x28+x33+x34 N= 71 d=0 T= 1+x3+x4+x9+x10+x13+x15+x16+x17+x18+x20+x21+x22+x23+x24+x25+x27+x28+x29+x32+x36 C= 1+x1+x3+x5+x10+x11+x12+x13+x14+x19+x23+x24+x27+x32+x34+x35+x36 l= 36 m= 69 b= 1+x3+x4+x8+x10+x11+x13+x14+x15+x16+x17+x18+x19+x20+x21+x24+x27+x28+x33+x34 N= 72 d=1 T= 1+x1+x3+x5+x10+x11+x12+x13+x14+x19+x23+x24+x27+x32+x34+x35+x36 C= 1+x1+x5+x6+x7+x10+x12+x16+x17+x18+x20+x21+x22+x30+x31+x32+x34+x35+x37 l= 37 m= 72 b= 1+x1+x3+x5+x10+x11+x12+x13+x14+x19+x23+x24+x27+x32+x34+x35+x36 N= 73 d=1 T= 1+x1+x5+x6+x7+x10+x12+x16+x17+x18+x20+x21+x22+x30+x31+x32+x34+x35+x37 C= 1+x2+x4+x5+x7+x10+x11+x13+x14+x15+x16+x17+x18+x21+x22+x24+x25+x28+x30+x31+x32+x33+x34+x36 l= 37 m= 72 b= 1+x1+x3+x5+x10+x11+x12+x13+x14+x19+x23+x24+x27+x32+x34+x35+x36 N= 74 d=0 T= 1+x1+x5+x6+x7+x10+x12+x16+x17+x18+x20+x21+x22+x30+x31+x32+x34+x35+x37 C= 1+x2+x4+x5+x7+x10+x11+x13+x14+x15+x16+x17+x18+x21+x22+x24+x25+x28+x30+x31+x32+x33+x34+x36 l= 37 m= 72 b= 1+x1+x3+x5+x10+x11+x12+x13+x14+x19+x23+x24+x27+x32+x34+x35+x36 N= 75 d=1 T= 1+x2+x4+x5+x7+x10+x11+x13+x14+x15+x16+x17+x18+x21+x22+x24+x25+x28+x30+x31+x32+x33+x34+x36 C= 1+x2+x3+x5+x6+x7+x8+x10+x11+x18+x21+x24+x25+x26+x27+x28+x31+x32+x33+x34+x35+x36+x37+x38+x39 l= 39 m= 75 b= 1+x2+x4+x5+x7+x10+x11+x13+x14+x15+x16+x17+x18+x21+x22+x24+x25+x28+x30+x31+x32+x33+x34+x36 N= 76 d=1 T= 1+x2+x3+x5+x6+x7+x8+x10+x11+x18+x21+x24+x25+x26+x27+x28+x31+x32+x33+x34+x35+x36+x37+x38+x39 C= 1+x1+x2+x7+x10+x12+x14+x15+x16+x17+x19+x21+x22+x23+x24+x27+x28+x29+x36+x38+x39 l= 39 m= 75 b= 1+x2+x4+x5+x7+x10+x11+x13+x14+x15+x16+x17+x18+x21+x22+x24+x25+x28+x30+x31+x32+x33+x34+x36 N= 77 d=0 T= 1+x2+x3+x5+x6+x7+x8+x10+x11+x18+x21+x24+x25+x26+x27+x28+x31+x32+x33+x34+x35+x36+x37+x38+x39 C= 1+x1+x2+x7+x10+x12+x14+x15+x16+x17+x19+x21+x22+x23+x24+x27+x28+x29+x36+x38+x39 l= 39 m= 75 b= 1+x2+x4+x5+x7+x10+x11+x13+x14+x15+x16+x17+x18+x21+x22+x24+x25+x28+x30+x31+x32+x33+x34+x36 N= 78 d=1 T= 1+x1+x2+x7+x10+x12+x14+x15+x16+x17+x19+x21+x22+x23+x24+x27+x28+x29+x36+x38+x39 C= 1+x1+x2+x3+x5+x8+x12+x13+x15+x18+x20+x22+x23+x25+x29+x31+x33+x34+x35+x37+x38 l= 40 m= 78 b= 1+x1+x2+x7+x10+x12+x14+x15+x16+x17+x19+x21+x22+x23+x24+x27+x28+x29+x36+x38+x39 N= 79 d=0 T= 1+x1+x2+x7+x10+x12+x14+x15+x16+x17+x19+x21+x22+x23+x24+x27+x28+x29+x36+x38+x39 C= 1+x1+x2+x3+x5+x8+x12+x13+x15+x18+x20+x22+x23+x25+x29+x31+x33+x34+x35+x37+x38 l= 40 m= 78 b= 1+x1+x2+x7+x10+x12+x14+x15+x16+x17+x19+x21+x22+x23+x24+x27+x28+x29+x36+x38+x39 N= 80 Input =01010011011010000110111101110010011101000010000001010100011001010111001101110100 Panjangnya =80 Init =0010111001001110111101100001011011001010

Polinomial=1+x1+x2+x3+x5+x8+x12+x13+x15+x18+x20+x22+x23+x25+x29+x31+x33+x34+x35+x37+x38 GF2 Binary=111101001000110100101011010001010111011

Generate Process... Mesin=111101001000110100101011010001010111011 Init =0010111001001110111101100001011011001010 Register=0001011100100111011110110000101101100101 Out=0 feedback ke=1 Register=0000101110010011101111011000010110110010 Out=1 feedback ke=2 Register=1000010111001001110111101100001011011001 Out=0 feedback ke=3 Register=0100001011100100111011110110000101101100 Out=1 feedback ke=4 Register=0010000101110010011101111011000010110110 Out=0 feedback ke=5 Register=0001000010111001001110111101100001011011 Out=0 feedback ke=6 Register=0000100001011100100111011110110000101101 Out=1 feedback ke=7 Register=0000010000101110010011101111011000010110 Out=1 feedback ke=8 Register=0000001000010111001001110111101100001011 Out=0 feedback ke=9 Register=1000000100001011100100111011110110000101 Out=1 feedback ke=10 Register=0100000010000101110010011101111011000010 Out=1 feedback ke=11 Register=1010000001000010111001001110111101100001 Out=0 feedback ke=12 Register=0101000000100001011100100111011110110000 Out=1 feedback ke=13 Register=1010100000010000101110010011101111011000 Out=0 feedback ke=14 Register=0101010000001000010111001001110111101100 Out=0 feedback ke=15 Register=0010101000000100001011100100111011110110 Out=0 feedback ke=16 Register=0001010100000010000101110010011101111011 Out=0 feedback ke=17 Register=1000101010000001000010111001001110111101 Out=1 feedback ke=18 Register=1100010101000000100001011100100111011110 Out=1 feedback ke=19 Register=0110001010100000010000101110010011101111 Out=0 feedback ke=20 Register=0011000101010000001000010111001001110111 Out=1 feedback ke=21 Register=1001100010101000000100001011100100111011 Out=1 feedback ke=22 Register=0100110001010100000010000101110010011101 Out=1 feedback ke=23 Register=1010011000101010000001000010111001001110 Out=1 feedback ke=24 Register=0101001100010101000000100001011100100111 Out=0 feedback ke=25 Register=1010100110001010100000010000101110010011 Out=1 feedback ke=26 Register=1101010011000101010000001000010111001001 Out=1 feedback ke=27 Register=1110101001100010101000000100001011100100 Out=1 feedback ke=28 Register=0111010100110001010100000010000101110010 Out=0 feedback ke=29 Register=0011101010011000101010000001000010111001 Out=0 feedback ke=30 Register=1001110101001100010101000000100001011100 Out=1 feedback ke=31 Register=1100111010100110001010100000010000101110 Out=0 feedback ke=32 Register=0110011101010011000101010000001000010111 Out=0 feedback ke=33 Register=1011001110101001100010101000000100001011 Out=1 feedback ke=34 Register=1101100111010100110001010100000010000101 Out=1 feedback ke=35 Register=1110110011101010011000101010000001000010 Out=1 feedback ke=36 Register=0111011001110101001100010101000000100001 Out=0 feedback ke=37 Register=1011101100111010100110001010100000010000 Out=1 feedback ke=38 Register=0101110110011101010011000101010000001000 Out=0 feedback ke=39 Register=0010111011001110101001100010101000000100 Out=0 feedback ke=40 Register=1001011101100111010100110001010100000010 Out=0 feedback ke=41 Register=0100101110110011101010011000101010000001 Out=0 feedback ke=42 Register=1010010111011001110101001100010101000000 Out=1 feedback ke=43 Register=0101001011101100111010100110001010100000 Out=0 feedback ke=44 Register=1010100101110110011101010011000101010000 Out=0 feedback ke=45 Register=0101010010111011001110101001100010101000 Out=0 feedback ke=46 Register=1010101001011101100111010100110001010100 Out=0 feedback ke=47 Register=0101010100101110110011101010011000101010 Out=0 feedback ke=48 Register=1010101010010111011001110101001100010101 Out=0 feedback ke=49 Register=0101010101001011101100111010100110001010 Out=1 feedback ke=50 Register=0010101010100101110110011101010011000101 Out=0 feedback ke=51 Register=0001010101010010111011001110101001100010 Out=1 feedback ke=52 Register=0000101010101001011101100111010100110001 Out=0 feedback ke=53 Register=1000010101010100101110110011101010011000 Out=1 feedback ke=54 Register=1100001010101010010111011001110101001100 Out=0 feedback ke=55 Register=0110000101010101001011101100111010100110 Out=0 feedback ke=56 Register=0011000010101010100101110110011101010011 Out=0 feedback ke=57 Register=0001100001010101010010111011001110101001 Out=1 feedback ke=58 Register=1000110000101010101001011101100111010100 Out=1 feedback ke=59 Register=0100011000010101010100101110110011101010 Out=0 feedback ke=60 Register=1010001100001010101010010111011001110101 Out=0 feedback ke=61 Register=1101000110000101010101001011101100111010 Out=1 feedback ke=62 Register=1110100011000010101010100101110110011101 Out=0 feedback ke=63 Register=0111010001100001010101010010111011001110 Out=1 feedback ke=64 Register=1011101000110000101010101001011101100111 Out=0 feedback ke=65 Register=0101110100011000010101010100101110110011 Out=1 feedback ke=66 Register=0010111010001100001010101010010111011001 Out=1 feedback ke=67 Register=0001011101000110000101010101001011101100 Out=1 feedback ke=68 Register=0000101110100011000010101010100101110110 Out=0 feedback ke=69 Register=1000010111010001100001010101010010111011 Out=0 feedback ke=70 Register=1100001011101000110000101010101001011101 Out=1 feedback ke=71 Register=1110000101110100011000010101010100101110 Out=1 feedback ke=72 Register=1111000010111010001100001010101010010111 Out=0 feedback ke=73 Register=0111100001011101000110000101010101001011 Out=1 feedback ke=74 Register=0011110000101110100011000010101010100101 Out=1 feedback ke=75 Register=0001111000010111010001100001010101010010 Out=1 feedback ke=76 Register=1000111100001011101000110000101010101001 Out=0 feedback ke=77 Register=1100011110000101110100011000010101010100 Out=1 feedback ke=78 Register=0110001111000010111010001100001010101010 Out=0 feedback ke=79 Register=0011000111100001011101000110000101010101 Out=0 feedback ke=80 01010011011010000110111101110010011101000010000001010100011001010111001101110100 010100110110100001101111011100100111010000100000010101000110010101110011011101 Short Test

• Welcome to crypto.stackexchange - Unfortunately the format of your answer(s) are likely to be unhelpful, as it consists of information that is effectively impossible to read and follow along with. The question did ask for a numerical example, but it would be far more helpful to give an example using smaller and more readable values, along with an explanation rather than just a dump of values. Commented Feb 4, 2019 at 15:19