English

A class of $q$-ary linear codes derived from irreducible cyclic codes

Information Theory 2016-04-18 v2 math.IT

Abstract

Recently, linear codes with a few weights were widely investigated due to their applications in secret sharing schemes and authentication schemes. In this letter, we present a class of qq-ary linear codes derived from irreducible cyclic codes with qq a prime power. We use Gauss sums to represent its Hamming weights and obtain the bounds of its minimum Hamming distance. In some cases, we explicitly determine its weight distributions which generalize some known results. It is quite interesting that many new codes obtained in this letter are optimal according to some bounds on linear codes.

Keywords

Cite

@article{arxiv.1511.09174,
  title  = {A class of $q$-ary linear codes derived from irreducible cyclic codes},
  author = {Ziling Heng and Qin Yue},
  journal= {arXiv preprint arXiv:1511.09174},
  year   = {2016}
}

Comments

This paper has been withdraw because a part of the main results has been reported before

R2 v1 2026-06-22T11:57:02.395Z