On the parameters of a class of narrow sense primitive BCH codes

Abstract

The last decades, mark an accelerated progression in the determination of the parameters of the primitive BCH codes. Indeed, BCH codes are powerful in terms of decoding. They are applied in several fields such as: satellite communications, cryptography, compact disk drives... and have good structural properties. Nevertheless, the dimension and the minimum distance of those codes aren't known, in general. In this paper, we present a class of narrow sense primitive BCH codes of designed distance $\delta_{_4}=(q-1)q^{^{m-1}}-1-q^{\lfloor \frac{m+3}{2 }\rfloor}.$ Also, we investigate their Bose distance and the dimension.

Received: 14 February 2022 | Accepted: 27 January 2023