A class of BCH codes with length q2m-1/q+1

作者：Pang, Binbin^*; Kai, Xiaoshan; Gao, Jun

来源：APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2023, s00200-023-00637-z.

DOI：10.1007/s00200-023-00637-z

• Cyclotomic coset
• Coset leader
• BCH code

As an important class of cyclic codes, BCH codes are widely employed in satellite communications, DVDs, CD, DAT etc. In this paper, we determine the dimension of BCH codes of length q(2m)-1/q+1 over the finite fields F-q. We settle a conjecture about the largest q-cyclotomic coset leader modulo n which was proposed by Wu et al. We also get the second largest q-cyclotomic coset leader modulo n if m is odd. Moreover, we investigate the parameters of C-(n,C-q,C-delta i) (C-(n,C-q,C-delta i))(perpendicular to) for i = 1, 2 and C-(n,C-q,C-delta) C-(n,C-q,C-delta))(perpendicular to)) for 2 <= delta <= q - 1. What's more, we obtain many (almost) optimal codes.