Some new results on dimension and Bose distance for various classes of BCH codes

Abstract

In this paper, we give the dimension and the minimum distance of two subclasses of narrow-sense primitive BCH codes over Fq with designed distance δ=aqm−1−1(resp. δ=aqm−1q−1) for all 1≤a≤q−1, where q is a prime power and m>1 is a positive integer. As a consequence, we obtain an affirmative answer to two conjectures proposed by C. Ding in 2015. Furthermore, using the previous part, we extend some results of Yue and Hu [16], and we give the dimension and, in some cases, the Bose distance for a large designed distance in the range [aqm−1q−1,aqm−1q−1+T] for 0≤a≤q−2, where T=qm+12−1 if m is odd, and T=2qm2−1 if m is even.