Computing the distance distribution of systematic non-linear codes
Discrete Mathematics
2016-04-01 v1 Information Theory
math.IT
Abstract
The most important families of non-linear codes are systematic. A brute-force check is the only known method to compute their weight distribution and distance distribution. On the other hand, it outputs also all closest word pairs in the code. In the black-box complexity model, the check is optimal among closest-pair algorithms. In this paper we provide a Groebner basis technique to compute the weight/distance distribution of any systematic non-linear code. Also our technique outputs all closest pairs. Unlike the check, our method can be extended to work on code families.
Keywords
Cite
@article{arxiv.0909.1626,
title = {Computing the distance distribution of systematic non-linear codes},
author = {Eleonora Guerrini and Emmanuela Orsini and Massimiliano Sala},
journal= {arXiv preprint arXiv:0909.1626},
year = {2016}
}