Construction of Partial-Unit-Memory MDS Convolutional Codes

Maximum-distance separable (MDS) convolutional codes form an optimal family of convolutional codes, the study of which is of great importance. There are very few general algebraic constructions of MDS convolutional codes. In this paper, we construct a large family of partial-unit-memory MDS convolutional codes over $ \mathbb {F}_{q}$ with flexible parameters. Compared with the previous work, the field size $q$ required to define these codes is much smaller. The construction also leads to many new strongly MDS convolutional codes, an important subclass of MDS convolutional codes. Some examples are presented at the end of this paper.