Parameters of Several Classes of BCH Codes

Author

Ding, Cunsheng

Author_Institution

Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hong Kong

Volume

61

Issue

10

fYear

2015

Firstpage

5322

Lastpage

5330

Abstract

Because of their efficient encoding and decoding algorithms, cyclic codes—an interesting class of linear codes—are widely used in communication systems, storage devices, and consumer electronics. BCH codes form a special class of cyclic codes, and are usually among the best cyclic codes. A subclass of good BCH codes is the narrow-sense primitive BCH codes. However, the dimension and minimum distance of these codes are not known in general. The main objective of this paper is to study the dimension and minimum distances of a subclass of the narrow-sense primitive BCH codes with design distance $\\delta =(q-\\ell _{0})q^{m-\\ell _{1}-1}-1$ for certain pairs $(\\ell _{0}, \\ell _{1})$ , where $0 \\leq \\ell _{0} \\leq q-2$ and $0 \\leq \\ell _{1} \\leq m-1$ . The parameters of other related classes of BCH codes are also investigated, and some open problems are proposed in this paper.

Keywords

Decoding; Generators; Indexes; Linear codes; Polynomials; Reed-Solomon codes; BCH codes; cyclic codes; linear codes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2015.2470251

Filename

7210201