A class of constacyclic BCH codes and new quantum codes

A class of constacyclic BCH codes and new quantum codes Constacyclic BCH codes have been widely studied in the literature and have been used to construct quantum codes in latest years. However, for the class of quantum codes of length $$n=q^{2m}+1$$ n = q 2 m + 1 over $$F_{q^2}$$ F q 2 with q an odd prime power, there are only the ones of distance $$\delta \le 2q^2$$ δ ≤ 2 q 2 are obtained in the literature. In this paper, by a detailed analysis of properties of $$q^{2}$$ q 2 -ary cyclotomic cosets, maximum designed distance $$\delta _\mathrm{{max}}$$ δ max of a class of Hermitian dual-containing constacyclic BCH codes with length $$n=q^{2m}+1$$ n = q 2 m + 1 are determined, this class of constacyclic codes has some characteristic analog to that of primitive BCH codes over $$F_{q^2}$$ F q 2 . Then we can obtain a sequence of dual-containing constacyclic codes of designed distances $$2q^2<\delta \le \delta _\mathrm{{max}}$$ 2 q 2 < δ ≤ δ max . Consequently, new quantum codes with distance $$d > 2q^2$$ d > 2 q 2 can be constructed from these dual-containing codes via Hermitian Construction. These newly obtained quantum codes have better code rate compared with those constructed from primitive BCH codes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

A class of constacyclic BCH codes and new quantum codes

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Springer US
Copyright © 2017 by Springer Science+Business Media New York
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
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