Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …

Linear codes are considered over the ring Z 4+ u Z 4, a non-chain extension of Z 4. Lee
weights, Gray maps for these codes are defined and MacWilliams identities for the complete …

We describe G-codes, which are codes that are ideals in a group ring, where the ring is a
finite commutative Frobenius ring and G is an arbitrary finite group. We prove that the dual of …

We introduce a bordered construction over group rings for self-dual codes. We apply the
constructions over the binary field and the ring F 2+ u F 2, using groups of orders 9, 15, 21 …

In this paper, we introduce a new bordered construction for self-dual codes using group
rings. We consider constructions over the binary field, the family of rings R k and the ring F …

In this work, we propose a modified four circulant construction for self-dual codes and a
bordered version of the construction using the properties of λ-circulant and λ-reverse …

In this work, we study construction techniques of formally self-dual codes over the infinite
family of rings R k= F 2 [u 1, u 2,…, uk]/< ui 2= 0, uiuj= ujui>. These codes give rise to binary …

In this paper, we show that one can construct a $ G $-code from group rings that is
reversible. Specifically, we show that given a group with a subgroup of order half the order of …

In this work we introduce a wide generalization of dynamical systems over graphs, by
considering that the states of the entities can take values in an arbitrary Boolean algebra …

In this work, we define composite matrices which are derived from group rings. We extend
the idea of G-codes to composite G-codes. We show that these codes are ideals in a group …