On shortened and punctured cyclic codes
Abstract
The problem of identifying whether the family of cyclic codes is asymptotically good or not is a long-standing open problem in the field of coding theory. It is known in the literature that some families of cyclic codes such as BCH codes and Reed-Solomon codes are asymptotically bad, however in general the answer to this question is not known. A recent result by Nelson and Van Zwam shows that, all linear codes can be obtained by a sequence of puncturing and/or shortening of a collection of asymptotically good codes~\cite{Nelson_2015}. In this paper, we prove that any linear code can be obtained by a sequence of puncturing and/or shortening of some cyclic code. Therefore the result that all codes can be obtained by shortening and/or puncturing cyclic codes leaves the possibility open that cyclic codes are asymptotically good.
Keywords
Cite
@article{arxiv.1705.09859,
title = {On shortened and punctured cyclic codes},
author = {Arti Yardi and Ruud Pellikaan},
journal= {arXiv preprint arXiv:1705.09859},
year = {2017}
}