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) [(q + 1, q − 4i + 3, 1; 2, 2i + 2)]q , where q ≥ 5 is an odd prime power and 2 ≤ i ≤ (q − 1)/2; (ii) [( q 2 +1 10 , q 2 +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.