In this paper, we study skew cyclic codes over the ring R = Fq + uFq + vFq + uvFq, where u 2 = u, v2 = v, uv = vu, q = p and p is an odd prime. We investigate the structural properties of skew cyclic codes over R through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length n over R.

This article discusses skew generalized quasi-cyclic codes over any finite field F with Galois automorphism θ. This is a generalization of quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes since their lengths do not have to be multiples of the index. After a brief description of the skew polynomial ring F[x; θ], we show that a skew general...

Tables are presented of good ternary and quaternary codes and they are used in the construction of dense sphere packings. Results include 1) tables of the best ternary and quaternary constacyclic codes (including cyclic codes) up to block length 50, 2 ) a class of optimal [ n , 21 codes over GF(q), 3) the ( U + U + w I2u + U I U ) construction, a new ternary code construction technique that can...

Let R be a finite commutative chain ring, D 2 n the dihedral group of size and [ ] ring. In this paper, we completely characterize left ideals (called -codes) when gcd ( c h r ) , = 1 . way, explore structure some skew-cyclic codes length over also × S where is an isomorphic copy As particular result, give cyclic case F p m Galois field, classification for N -codes any positive integer both cas...

In the present paper, we study skew cyclic codes over the ring $F_{q}+vF_{q}+v^2F_{q}$, where $v^3=v,~q=p^m$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ using decomposition method. By defining a Gray map from $F_{q}+vF_{q}+v^2F_{q}$ to $F_{q}^3$, it has been proved that the Gray image of a skew cyclic code of length $n$ ove...

Let Fpm be a finite field with cardinality p and R = Fpm + uFpm with u = 0. We aim to determine all α + uβ-constacyclic codes of length np over R, where α, β ∈ Fpm , n, s ∈ N+ and gcd(n, p) = 1. Let α0 ∈ F ∗ pm and α s 0 = α. The residue ring R[x]/〈x np − α − uβ〉 is a chain ring with the maximal ideal 〈x − α0〉 in the case that x n − α0 is irreducible in Fpm[x]. If x−α0 is reducible in Fpm[x], w...