A class of $p$-ary cyclic codes and their weight enumerators
Long Yu, Hongwei Liu

TL;DR
This paper investigates the weight distribution of a specific class of $p$-ary cyclic codes, extending previous results to new cases based on the parity of certain parameters, and provides explicit weight enumerators.
Contribution
It extends the analysis of cyclic codes' weight distribution to additional parameter cases, offering explicit formulas for their weight enumerators.
Findings
Determined weight distributions for new parameter cases.
Extended previous results to cover all cases of $rac{m}{ ext{gcd}(m,k)}$.
Provided explicit weight enumerators for the cyclic codes.
Abstract
Let , be positive integers such that , be an odd prime and be a primitive element of . Let and be the minimal polynomials of and over , respectively. In the case of odd , when is even, is odd or when is odd, Zhou et~al. in \cite{zhou} obtained the weight distribution of a class of cyclic codes over with parity-check polynomial . In this paper, we further investigate this class of cyclic codes over in the rest case of odd and the case of even . Moreover, we determine the weight distribution of cyclic codes .
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications
