We’re rewarding the question askers & reputations are being recalculated! Read more.

Questions tagged [coding-theory]

Coding theory studies the properties of codes and their fitness for specific applications, and typically involves the removal of redundancy and the detection and/or correction of errors in transmitted data.

8 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
3
votes
0answers
77 views

Words having weight near to minimum distance

I am studying the NP-Problem of the codes Syndrome Decoding. The formulation is show below. Input: a binary matrix $H$ of dimension $r \times n$ and a bit string $S$ of length $r$. Property: there ...
2
votes
0answers
27 views

Choosing the Bernoulli distribution for LPN encryption scheme

The symmetric-key encryption scheme from [1] is based on the LPN (learning parity with noise) problem. The definition of the problem is, informally, that the adversary cannot recover $\mathbf{s}$ from ...
2
votes
0answers
295 views

Convolution and catastrophic codes

i'm reading the article of Massey and Sain (here) and i cannot unserstand - what is "foreforward inversion"? I mean There is a description of circles in convolutional codes and a little bit ...
1
vote
0answers
39 views

Number of words in binary linear code starting with zero and unit

Is it true that in a binary linear code number of words, which start with zero, is always at least as much as words, which start with 1? I have no idea how to prove or disprove it. Can you give me a ...
1
vote
0answers
81 views

Ciphertext indistinguishability under a noisy channel w/ error correction

The objective is to broadcast information over a noisy digital channel (corruption rate of say, 10-20 %, where bits flip). Assume the broadcasting software is public and there is no possibility of ...
1
vote
0answers
67 views

Suggestion for proof of retrievability (via coding theory)

I want to build a fully open-source open-everything protocol/service for massively-distributed shared storage (P2P). I came up with a suggestion for a proof-of-retrievability scheme, but I would like ...
0
votes
0answers
22 views

Is it possibe to extend DGK method of comparion two integers to $d$-ary settings?

In [1], a method for comparing two integers is described by using polynomial operations related to the binary representations of the given two integers. The method is re-phrased as follows: Given the ...
0
votes
0answers
24 views

What are dual codes and the codewords denoted by these dual codes in terms of trace?

I am currently reading a research paper (linked below) that mentions "Consider only maps that vanish at 0, their short codes $C_f$ and their duals $C_f^\perp$. The duals can be written as $C_f^\perp = ...