Complete b-symbol weight distribution of some irreducible cyclic codes

DOI10.1007/S10623-022-01030-6arXiv2110.00805WikidataQ114849766 ScholiaQ114849766MaRDI QIDQ6379213

Minjia Shi, Ferruh Özbudak, Hongwei Zhu

Publication date: 2 October 2021

Abstract: Recently, $b$-symbol codes are proposed to protect against $b$-symbol errors in $b$-symbol read channels. It is an interesting subject of study to consider the complete $b$-symbol weight distribution of cyclic codes since $b$-symbol metric is a generalization for Hamming metric. The complete $b$-symbol Hamming weight distribution of irreducible codes is known in only a few cases. In this paper, we give a complete $b$-symbol Hamming weight distribution of a class of irreducible codes with two nonzero $b$-symbol Hamming weights.

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Cyclic codes (94B15)

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