On weight spectrum of linear codes
Information Theory
2023-03-30 v1 Combinatorics
math.IT
Abstract
We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear codes has a uniform weight spectrum if the number of vectors from codes with weight grows to infinity. We find an example of a sequence of linear codes such that the dimension of the code is the half of the codelength but it has not a uniform weight spectrum. This example generates eigenfunctions of the Fourier transform with minimal support and partial covering sets. Moreover, we generalize some MacWilliams-type identity. Keywords: weight distribution of code, dual code, MacWilliams identity, Fourier transform, partial covering array
Keywords
Cite
@article{arxiv.2107.14576,
title = {On weight spectrum of linear codes},
author = {Vladimir N. Potapov},
journal= {arXiv preprint arXiv:2107.14576},
year = {2023}
}