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

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, δ
₁
)
₄
and B(n,δ
₂
)
₄
that satisfies B
^⊥h
(n,δ
₁
)
₄
⊆ B(n,δ
₂
)
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.