New quantum codes constructed from quaternary BCH codes

Leng Riguang, Zhi Ma

Ping Li, Yancong Wei, Xiaoshan Kai +1 more

Ruihu Li, Genqi Xu, Qiang Fu +1 more

In this paper, we focus on construction of asymmetric quantum error-correcting codes (AQECCs) from quaternary narrow-sense BCH codes of code length n = 4m-1/3(m≥3 is an integer) via Calderbank-Shor-Steane construction. By a careful analysis on properties of cyclotomic cosets in the defining sets of two ingredient BCH codes B(n, δ1)4and B(n,δ2)4that satisfies B⊥h(n,δ1)4⊆ B(n,δ2)4used for constructing AQECCs, we derive new families of AQECCs with dz> δmaxs+ 1, and thus we can eliminate the unreasonable restriction dz≤ δmaxdevised in previous literature and obtain new AQECCs with greater asymmetry compared with the known results. Here δmaxsis the maximal designed distance of Hermitian dual-containing narrow-sense BCH codes of length n = 4m-1/3.

Jiayuan Zhang, Ping Li, Xiaoshan Kai +1 more

LI Rui-hu

A method of describing quaternary cyclic codes with 4-cyclotomic cosets of modulo odd n and generator polynomials is presented.A necessary and sufficient condition under which a quaternary cyclic code containing its dual code is given,thus generalizing the related known results on self-orthogonal simple root cyclic codes and on BCH codes to al quaternary cyclic codes.Using the relation of simple root cyclic codes and repeat root cyclic codes,the linear quantum codes that can be constructed from quaternary cyclic codes of short lengths are determined.

Junli Wang, Ruihu Li, Yang Liu +1 more