In most of the cases, also generator matrices of those codes are provided. But as far as I see, the page doesn't provide means for the computation of the minimum distance of an arbitrary linear code.

Jun 18, 2016 · 3 Given a set $\mathcal {C}$ of codewords, before we can construct a generator matrix, we need to verify that $\mathcal {C}$ is a linear subspace - ie, the sum (and also scalar multiples in …

A set of Walsh functions of length $2^n$ may be regarded as set of $2^n$ binary code words of length $2^n$ bits that are maximally distant, i.e. each word is distance $2^ {n−1}$ from all others.

Oct 8, 2020 · According to this page, there should be a code of length 20 with hamming distance 6 and between 2048-2279 codewords (or in other words, that contains at least $2^ {11}$ words, meaning …

Oct 21, 2015 · Finding generator matrix for binary linear code given parity check matrix Ask Question Asked 10 years, 1 month ago Modified 8 years, 2 months ago

Dec 2, 2014 · I need to find the Generator and Parity check matrix of a binary cyclic [9,2] code. If I calculated right, the Generator polynomial is x^7 + x^6 + x^4 + x^3 + x + 1 and the check polynomial …

May 14, 2017 · Generator matrix of a binary Goppa code Ask Question Asked 8 years, 4 months ago Modified 6 years, 2 months ago

How is a Generator Matrix for a (7, 4) Hamming code created? Ask Question Asked 8 years, 10 months ago Modified 2 years, 10 months ago

Apr 12, 2013 · By duality, this is a check matrix of a binary $ (15,11)$ Hamming code. For general alphabets $\mathbb {F}_q$, you have to select a system of projective representatives of the non-zero …

I need to prove the following: Let C be a binary cyclic Hamming code; we add a parity check at the end of every code word and get an extended (not necessarily cyclic) code. We need to prove that ...