Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11024745 | Finite Fields and Their Applications | 2019 | 25 Pages |
Abstract
Under research for nearly sixty years, Bose-Chaudhuri-Hocquenghem (BCH) codes have played increasingly important roles in many applications such as communication, data storage and information security. However, the dimension and minimum distance of BCH codes have been seldom solved by now because of their intractable characteristics. The objective of this paper is to study the dimensions of some binary BCH codes with length n=2m+1. Many new techniques are employed to investigate the coset leaders modulo n. For m=2t+1,4t+2,8t+4 and mâ¥10, the first five largest coset leaders modulo n are determined, and the dimensions of some BCH codes of length n with designed distance δ>2âm2â are presented. These new skills and results may be helpful to study other types of cyclic codes over finite fields.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yang Liu, Ruihu Li, Qiang Fu, Liangdong Lu, Yi Rao,