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arXiv · 1706.09188

Optimal quinary cyclic codes with minimum distance four

JinMei Fan
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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.

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JinMei Fan. 2018-01-20. Optimal quinary cyclic codes with minimum distance four. https://arxiv.org/abs/1706.09188

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