NEW QUANTUM CODES CONSTRUCTED FROM A CLASS OF IMPRIMITIVE BCH CODES

作者：Liu, Yang^*; Ma, Yuena; Feng, Youqian; Li, Ruihu

来源：International Journal of Quantum Information, 2013, 11(1): 1350006.

DOI：10.1142/S0219749913500068

• Cyclotomic coset
• imprimitive BCH (Bose-Chaudhuri-Hocquenghem) code
• dual containing code
• dimension
• quantum code

By a careful analysis on cyclotomic cosets, the maximal designed distance delta(new) of narrow-sense imprimitive Euclidean dual containing q-ary BCH code of length n = (q - 1) q(il)-1/q(i)-1 is determined, where q is a prime power and l is odd. Our maximal designed distance delta(new) of dual containing narrow-sense BCH codes of length n improves upon the lower bound delta(max) for maximal designed distances of dual containing narrow-sense BCH codes given by Aly et al. [IEEE Trans. Inf. Theory 53 (2007) 1183]. A series of non-narrow-sense dual containing BCH codes of length n, including the ones whose designed distances can achieve or exceed delta(new), are given, and their dimensions are computed. Then new quantum BCH codes are constructed from these non-narrow-sense imprimitive BCH codes via Steane construction, and these new quantum codes are better than previous results in the literature.

• 出版日期2013-2
• 单位中国人民解放军空军工程大学