Semiregular Convolutional Codes: Definition, Structure, and Examples

In this paper, the set of sequences of q-ary n-tuples is endowed with the structure of a module over an appropriate algebra. Then, semiregular convolutional codes are introduced as submodules; such codes indeed have the property that they admit a semiregular automorphism group. The structure and properties of the codes are investigated in detail. In particular, some canonical generators are exhibited that can be used to construct a minimal encoder. Finally, several examples are given which show that there actually exist good semiregular convolutional codes.