New quantum constacyclic codes

Hermitian dual-containing constacyclic BCH codes and related quantum codes of length $\frac{q^{2m}-1}{q+1}$

“…From these tables, we can see that our quantum codes have better performance. Moreover, for the maximum design distance δ max in this paper, δ A in [2], δ Y in [24], and δ L in [25], it is easy to infer that δ max > (q − 1)δ A , δ max = δ Y or δ Y + 1, and δ max = δ L or δ L + 1. It means that for length n = q 2m −1 q+1 (m is even), the Hermitian dual containing constacyclic BCH codes studied in this paper have relatively large design distance.…”

“…We found that some optimal or almost optimal codes can be obtained from the narrowsense constacyclic BCH codes of length n = q 2m −1 q+1 with special values of q and m (see Remark 2 in Subsection 3.2). In addition, some quantum codes constructed from narrowsense constacyclic BCH codes of length n = q 2m −1 q+1 have better parameters compared to some known results studied in the literature [2,17,18,24,25,35]. Thus, this family of constacyclic BCH codes deserve to be investigated further.…”

“…Definition 1 [25,27] Assume that gcd(n, q) = 1. Let C = g(x) be an η-constacyclic code of length n over F q 2 , where η is a primitive rth root of unity.…”

“…Yves Edel provided code tables of some good quantum twisted codes for q ≤ 9 and length up to 1000 [17]. In [25], Li et al gave two classes of quantum codes from non-narrow-sense constacyclic codes, a class of which are with lengths n = (q−1)(q 2 +1) b , where b | q − 1. Fixing the code lengths n = q 2m −1 q+1 (m ≥ 2 even), we compare our quantum codes with known ones in [2,17,24,25].…”

“…In [25], Li et al gave two classes of quantum codes from non-narrow-sense constacyclic codes, a class of which are with lengths n = (q−1)(q 2 +1) b , where b | q − 1. Fixing the code lengths n = q 2m −1 q+1 (m ≥ 2 even), we compare our quantum codes with known ones in [2,17,24,25]. Their results are provided as follows.…”