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Optimal quinary cyclic codes with minimum distance four (1706.09188v2)
Published 28 Jun 2017 in cs.IT and math.IT
Abstract: In this paper, by analyzing solutions of certain equations in the finite field $\mathbb{F}_{5m}$, three classes of new optimal quinary cyclic codes with parameters $[5m-1,5m-2m-2,4]$ 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.