Convolutional Codes Derived From Group Character Codes

Constructions of (classical) convolutional codes and their corresponding properties have been presented in the literature [1, 3–8, 12, 15–20]. In [3], the author constructed an algebraic structure for convolutional codes. Addressing the construction of maximum-distance-separable (MDS) convolutional codes (in the sense that the codes attain the generalized Singleton bound introduced in [18, Theorem 2.2]), there exist interesting papers in the literature [5, 18, 20]. Concerning the optimality with respect to other bounds we have [16, 17], and in [4], Strongly MDS convolutional codes were constructed. In [1, 8, 12, 19], the authors presented constructions of convolutional BCH codes. In [6], doubly-cyclic convolutional codes were constructed and in [7], the authors described cyclic convolutional codes by means of the matrix ring. In this paper we construct families of unit memory as well as multi-memory convolutional codes, although it is well known that unit memory codes have large free distance when compared to multi-memory codes of same rate ( see [13]). Our constructions are performed algebraically and not by computation search. Consequently, we do not restrict ourselves in constructing only few specific codes. To do so we apply the famous method proposed by Piret [15] and recently generalized by Aly et al. [1, Theorem 3], which consists in the construction of convolutional codes derived from block codes. The block codes utilized in our construction is the subclass of 2-group character codes introduced