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 = 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 and B(n, δ2)4 that satisfies B┴(n, δ1)4 ⊆ B (n, δ2)4 used for constructing AQECCs, we derive new families of AQECCs with dz > δmax + 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 δmax is the maximal designed distance of Hermitian dual-containing narrow-sense BCH codes of length n = 4m -- 1/3.
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