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

In this paper, we give the dimension and the minimum distance of two subclasses of narrow-sense primitive BCH codes over F q with designed distance δ = a q m − 1 − 1 (resp. δ = a q m − 1 q − 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 a q m − 1 q − 1 , a q m − 1 q − 1 + T for 0 ≤ a ≤ q − 2 , where T = q m + 1 2 − 1 if m is odd, and T = 2 q m 2 − 1 if m is even. [ABSTRACT FROM AUTHOR]