In this paper we generalize coding theory of cyclic codes over finite fields to skew polynomial rings over finite rings. Codes that are principal ideals in quotient rings of skew polynomial rings by two sided ideals are studied. Next we consider skew codes of endomorphism type and derivation type. And we give some examples.

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...

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...

Quantum error-correcting codes play an important role in both quantum communication and quantum computation. It has experienced a great progress since the establishment of the connections between quantum codes and classical codes (see [4]). It was shown that the construction of quantum codes can be reduced to that of classical linear error-correcting codes with certain self-orthogonality proper...

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...

Article history: Received 13 February 2014 Accepted 18 April 2014 Available online 2 June 2014 Communicated by Gary L. Mullen