More classes of optimal quinary cyclic codes of form $${\mathcal {C}}_{(1,e,s)}$$
Applicable Algebra in Engineering, Communication and Computing(2023)
Abstract
Cyclic codes are an important subclass of linear codes. In this paper, we investigate the construction of quinary cyclic codes with parameters
$$[5^{m}-1, 5^{m}-2m-2, 4]$$
and eight new classes optimal quinary cyclic codes of form
$${\mathcal {C}}_{(1,e,s)}$$
are presented by discussing the solutions of certain equations over
$${\mathbb {F}}_{5^{m}}$$
.
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Key words
Cyclic code,Optimal code,Quinary code,Minimum distance
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