A class of narrowsense BCH codes over mathbb F_q of length fracqm12. BCH codes with efficient encoding and decoding algorithms have many applications in communications, cryptography and combinatorial design. This paper studies a class of linear codes of length ( fracqm12) over (mathbb F_q) with special trace representation, where q is an odd prime power. With the help of the inner distributions of some subsets of association schemes of quadratic forms, we determine the weight enumerators of these codes. Determining some cyclotomic coset leaders (delta _i) of cyclotomic cosets modulo ( fracqm12), we prove that narrowsense BCH codes of length ( fracqm12) with designed distance (delta _ifracqmqm121fracq lfloor fracm32 rfloor i12) have the corresponding trace representation, and have the minimal distance (ddelta _i) and the Bose distance (d_Bdelta _i), where (1le ile lfloor fracm116 rfloor ).

New quantum codes from two linear codes A CSS quantum code is succinctly represented as a pair of linear codes (C_1 ,C_2perp ) over finite fields mathbb F_pe with C_2perp subset C_1, where p is a prime and e is a positive integer. In this paper, we present two criteria of the C_2perp _ssubset C_1 , where C_2perp _s denotes the sGalois dual of C_2 and 0le s u003ce. Then, using the two criteria, we construct some new quantum codes and a class of new quantum maximumdistanceseparable (quantum MDS) codes. In addition, our obtained quantum MDS codes have parameters better than the ones available in the literature.