A construction of MDS quantum convolutional codes - Zhang, Guanghui (2015)
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+1)/10 , (q2+1)/10 - 4i, 1; 2, 2i + 3)]q, where q is an odd prime power with the form q = 10m + 3 or 10m + 7 (m ≥ 2), and 2 ≤ i ≤ 2m - 1.