Parameters of two classes of LCD BCH codes

BCH codes are widely employed in data storage, communications systems, and consumer electronics. A new application of LCD codes in cryptography was found recently. It is known that LCD codes are asymptotically good. LCD cyclic codes were referred to as reversible cyclic codes in the literature. The objective of this paper is to construct a class of LCD codes, which are also BCH codes. The dimensions and the minimum distances of these LCD cyclic codes are investigated. We will also study a class of reversible BCH codes proposed in [13] and extend the results on their parameters. As a byproduct, the parameters of some primitive BCH codes will be analysed. Some of the codes are optimal or have the best known parameters.