Optimal quinary cyclic codes with minimum distance four

JinMei Fan

Optimal quinary cyclic codes with minimum distance four

Information Theory 2018-01-23 v2 math.IT

Authors: JinMei Fan

Abstract

In this paper, by analyzing solutions of certain equations in the finite field $\mathbb{F}_{5^m}$ , three classes of new optimal quinary cyclic codes with parameters $[5^m-1,5^m-2m-2,4]$ and two theorems are presented. With the help of the two theorems, perfect nonlinear monomials, almost perfect nonlinear monomials and a number of other monomials are used to construct more classes of new optimal quinary cyclic codes with the same parameters.

Keywords

coding theory maximum distance separable code sequence design

Cite

@article{arxiv.1706.09188,
  title  = {Optimal quinary cyclic codes with minimum distance four},
  author = {JinMei Fan},
  journal= {arXiv preprint arXiv:1706.09188},
  year   = {2018}
}

Comments

22 pages

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