The Hermitian Dual Codes of Several Classes of BCH Codes

被引:2
|
作者
Fan, Mengyuan [1 ,2 ]
Li, Chengju [1 ,2 ]
Ding, Cunsheng [3 ]
机构
[1] East China Normal Univ, MoE Engn Res Ctr Software Hardware Codesign Techno, Shanghai 200062, Peoples R China
[2] Southeast Univ, Natl Mobile Commun Res Lab, Nanjing 210096, Peoples R China
[3] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Hong Kong, Peoples R China
基金
中国国家自然科学基金;
关键词
BCH code; Hermitian dually-BCH code; cyclic code; linear code; PRIMITIVE BCH; MINIMUM DISTANCE; QUANTUM; BOSE;
D O I
10.1109/TIT.2023.3257123
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
As a special subclass of cyclic codes, BCH codes are usually among the best cyclic codes and have wide applications in communication and storage systems and consumer electronics. Let C be a q(2)-ary BCH code of length n with respect to an n-th primitive root of unity ,0 over an extension field of F(q)2, and let C-?H denote its Hermitian dual code, where q is a prime power. If both C and C-?H are a BCH code with respect to an n-th primitive root of unity ,0, then C is called a Hermitian duallyBCH code. The objective of this paper is to derive a necessary and sufficient condition for ensuring that two classes of narrow-sense BCH codes are Hermitian dually-BCH codes. As by-products, lower bounds on the minimum distances of the Hermitian dual codes of these BCH codes are developed, which improve the lower bounds documented in IEEE Trans. Inf. Theory, vol. 68, no. 2, pp. 953-964, 2022, in some cases.
引用
收藏
页码:4484 / 4497
页数:14
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