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 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 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 …

A classification of all four-circulant extremal codes of length 32 over 𝔽₂+ 𝑢𝔽₂ is done by
using four-circulant binary self-dual codes of length 32 of minimum weights 6 and 8. As Gray …

We consider quasi-cyclic codes over the ring F _2+ u F _2+ v F _2+ uv F _2 F 2+ u F 2+ v F
2+ uv F 2, a finite non-chain ring that has been recently studied in coding theory. The Gray …

In this work, we describe a construction in which we combine together the idea of a
bisymmetric matrix and group rings. Applying this construction over the ring F 4+ u F 4 …

This paper studies and classifies all binary self-dual [62, 31, 12] and [64, 32, 12] codes
having an automorphism of order 7 with 8 cycles. This classification is done by applying a …

We obtain extremal binary self-dual codes of parameters [64, 32, 12] as binary images of self-
dual codes over R 1, R 2 and R 3 by employing different methods. We then apply the …

In this paper, we use the graded ring construction to lift the extended binary Hamming code
of length 8 to R_k R k. Using this method we construct self-dual codes over R_3 R 3 of …

A lift of binary self-dual codes to the ring R< sub> 2 is described. By using this lift, a family of
self-dual codes over R< sub> 2 of length 17 are constructed. Taking the binary images of …