Addendum to "Generalized Permutations in Convolutional Codes"

where 7/denotes the set of integers. Obviously F(D) has the structure of a field. An (n, h) convolutional code C of memory span m over F, is the F(D) row space m of a k × n polynomial matrix G(D) = ~i=0 Gi Di, where each G i (0 ~ i ~ m) is a k × n matrix overF. The rank of G(D) overF(D) must be k. Recently (Piret, 1978) binary (6, 2) codes were obtained as an application of convolutional operators that preserve automorphisms. For m ~ {1, 2, 4}, codes were constructed that have the largest possible free distance dy (Piret, 1978; see Table 4). However for m = 3, the best upper bound on d s is 16, while no code was obtained with d s > 14. The present note was motivated by this flaw. The idea is to obtain binary (6, 2) codes by the concatenation of (2, 1) codes over GF(4). We refer to (Piret, 1978) for the details of our arguments.