Designed distances and parameters of new LCD BCH codes over finite fields

摘要

Let Fq be the finite field of q elements and n = q(m) - 1 with m a positive integer. In this paper we construct a class of BCH and LCD BCH codes of length n over Fqdocumentclass[12pt]{minimal} and investigate their dimensions and designed distance. Our results show that the designed distances of BCH and LCD BCH codes in this paper are larger than those in [11, Theorems 7, 10, 18, and 22]. It is viewed as a generalized result of [11].