New quantum codes derived from a family of antiprimitive BCH codes.

The Bose-Chaudhuri-Hocquenghem (BCH) codes have been studied for more than 57 years and have found wide application in classical communication system and quantum information theory. In this paper, we study the construction of quantum codes from a family of q²-ary BCH codes with length n = q2m + 1 (also called antiprimitive BCH codes in the literature), where q ≥ 4 is a power of 2 and m ≥ 2. By a detailed analysis of some useful properties about q²-ary cyclotomic cosets modulo n, Hermitian dual-containing conditions for a family of non-narrowsense antiprimitive BCH codes are presented, which are similar to those of q²-ary primitive BCH codes. Consequently, via Hermitian Construction, a family of new quantum codes can be derived from these dual-containing BCH codes. Some of these new antiprimitive quantum BCH codes are comparable with those derived from primitive BCH codes. [ABSTRACT FROM AUTHOR]