A Construction of MDS Quantum Convolutional Codes

In this paper, two new families of MDS quantum convolutional codes are constructed. The first one can be regarded as a generalization of [36, Theorem 6.5], in the sense that we do not assume that q≡1 (mod 4). More specifically, we obtain two classes of MDS quantum convolutional codes with parameters: (i) [(q2+1,q2−4i+3,1;2,2i+2)]q, where q≥5 is an odd prime power and 2≤i≤(q−1)/2; (ii) [(q2+110,q2+110−4i,1;2,2i+3)]q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[(\frac {q^{2}+1}{10},\frac {q^{2}+1}{10}-4i,1;2,2i+3)]_{q}$\end{document}, where q is an odd prime power with the form q=10m+3 or 10m+7 (m≥2), and 2≤i≤2m−1.