四川大学学报（自然科学版）2024，Vol.61Issue(6)：42-48,7.DOI:10.19907/j.0490-6756.2024.061003
关于一类BCH码的对偶码的注记
A note on the dual codes of a class of BCH codes
摘要
Abstract
Determining whether BCH codes and their dual codes are almost maximum distance separable(AMDS)codes is a significant topic in coding theory.Let q be a power of the prime p and let Fq be the finite field with q elements.Let C(q,n,δ,h)be a class of BCH codes of length n and designed distance δ.In 2020,Ding and Tang showed that both the BCH code C(q,q+1,3,1)and its dual are AMDS codes when q=3m,m≥2 is a positive integer.Recently,Qiang et al.presented a characterization for the dual code of an AMDS code to be an AMDS code.Furthermore,they use this characterization to show that the dual code of the BCH code C(q,q+1,3,4)is an AMDS code when q=3m,m≥3 being odd.In this paper,by using the characterization of Qiang et al.,we supply an alternative proof to the theorem of Ding and Tang that the dual of the BCH code C(q,q+1,3,1)is an AMDS code.关键词
BCH码/MDS码/AMDS码/对偶码Key words
BCH code/MDS code/AMDS code/Dual code分类
数理科学引用本文复制引用
韦华凯,陈龙,强诗瑗,谭千蓉..关于一类BCH码的对偶码的注记[J].四川大学学报（自然科学版）,2024,61(6):42-48,7.基金项目
国家自然科学基金(11771304) （11771304）
攀枝花学院2022年校级科研项目(攀学院[2022]65号-13) （攀学院[2022]65号-13）
太阳能技术集成及应用推广四川省高校重点实验室项目(TYNSYS-2022-C-02)} （TYNSYS-2022-C-02）
