I have been asked to create an LFSR with a polynomial of x^15 + x + 1 and i am confused where the tap sequence would go.
The examples I was given show a 4 bit tap sequence with two polynomials: x^3 + 1 and x^2 + 1. These were shown having tap at positions 0101 and 0101 respectively, where the bold represents the tap sequence.
I am confused about where the tap sequence would go for x^15 + x + 1, since in the first above example, there is 4 bits but taps are at either ends with the polynomial x^3+1. So how would x^15 be placed on a 15 bit LFSR? surly it would not fit? (x^14 + 1 being taps at either end of the 15 bit LFSR following the examples?)
I have written code for this also and have placed taps 000001111100000, which i think is the correct tap sequence, however this outputs only 14 bits, being way under what i estimated. 0s and 1s being different then mentioned above. This also doesnt match the 4 bit examples i was given which is confusing me very much.
Where am i going wrong, any advice on this would be appreciated, thanks.