Some new quantum codes from constacyclic codes

期刊论文
发表日期：

2024年1月2日

查看全文

Shanqi Pang,
Miaomiao Zhang,
Mengqian Chen,
Chaomeng Zhang

摘要

In this paper, let q be an odd prime power. Based on new constacyclic codes which contain their Hermitian duals and Hermitian construction, we construct some classes of quantum MDS codes and quantum codes. When $q\equiv 1\ \textrm{mod}\ 4$ $q \equiv 1 mod 4$ , x and y are a divisor of $q-1$ $q - 1$ and $q+1$ $q + 1$ , respectively, we can construct a class of new quantum codes of length $n=2xy\frac{q^{2m}-1}{q^2-1}$ $n = 2 x y \frac{q^{2 m} - 1}{q^{2} - 1}$ for odd $x,y,m\ge 3$ $x, y, m \geq 3$ . These codes have larger dimensions than existing codes. In addition, for q with the form $2am\pm \sqrt{(x^2+y^2)a-1}$ $2 a m \pm \sqrt{(x^{2} + y^{2}) a - 1}$ and odd x, y, a with $gcd(x,y)=1$ $g c d (x, y) = 1$ , we get some quantum MDS codes of length $n=\frac{q^2+1}{a}$ $n = \frac{q^{2} + 1}{a}$ .