The dual codes of negacyclic BCH codes of length qm+12

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-09 DOI:10.1016/j.disc.2025.114525

Yuqing Fu , Hongwei Liu

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引用次数: 0

Abstract

Negacyclic BCH codes form an important subclass of negacyclic codes and can produce optimal linear codes in many cases. The question of whether the dual code of a negacyclic BCH code is a negacyclic BCH code is, in general, very hard to answer. To investigate further the properties of the dual codes of negacyclic BCH codes, the concept of negacyclic dually-BCH codes is proposed in this paper and then the dual codes of narrow-sense negacyclic BCH codes of length

\frac{q^{m} + 1}{2}

over the finite field

F_{q}

are studied, where

q \equiv 3 (\mod 4)

. Some lower bounds on the minimum distances of the dual codes are established, which are very close to the true minimum distances of the dual codes in many cases. Sufficient and necessary conditions in terms of designed distances are presented to ensure that narrow-sense negacyclic BCH codes of length

\frac{q^{m} + 1}{2}

are negacyclic dually-BCH codes.

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长度为qm+12的负循环BCH码的对偶码

负环BCH码是负环码的一个重要子类，在许多情况下可以产生最优的线性码。一般来说，一个负循环BCH码的对偶码是否是一个负循环BCH码的问题是很难回答的。为了进一步研究负环BCH码的对偶码的性质，本文提出了负环对偶BCH码的概念，然后研究了长度为qm+12的狭义负环BCH码在有限域Fq上的对偶码，其中q≡3（mod4）。建立了对偶码最小距离的下界，在许多情况下，这些下界与对偶码的真实最小距离非常接近。从设计距离上给出了长度为qm+12的狭义负环BCH码为负环双BCH码的充要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.