Asymmetric Quantum Codes of Large Z - Distance Constructed from a Class of Quaternary Imprimitive BCH Codes

Abstract

In this paper, we focus on construction of asymmetric quantum error-correcting codes (AQECCs) from quaternary narrow-sense BCH codes of code length n = 4^m-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)₄ and B(n,δ₂)₄ that satisfies B^⊥h(n,δ₁)₄ ⊆ B(n,δ₂)₄ used for constructing AQECCs, we derive new families of AQECCs with d_z > δ_max^s + 1, and thus we can eliminate the unreasonable restriction d_z ≤ δ_max devised in previous literature and obtain new AQECCs with greater asymmetry compared with the known results. Here δ_max^s is the maximal designed distance of Hermitian dual-containing narrow-sense BCH codes of length n = 4^m-1/3.