We provide a new definition for the concept of skew in parallel asynchronous communications introduced in [2]. The new definition extends and strengthens previously known results on skew. We give necessary and sufficient conditions for codes that can tolerate a certain amount of skew under the new definition. We also extend the results to codes that can tolerate a certain amount of skew and det...

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

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...

Skew Hadamard designs (4n−1, 2n−1, n−1) are associated to order 4n skew Hadamard matrices in the natural way. We study the codes spanned by their incidence matrices A and by I +A and show that they are self-dual after extension (resp. extension and augmentation) over fields of characteristic dividing n. Quadratic Residues codes are obtained in the case of the Paley matrix. Results on the p−rank...

In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left R_{k}[x;\theta]-submodules of R_{k}[x;\theta]/\langle x^{n}-1\rangle and construct their generators and minimal generating sets. Also, an algorithm has been provided to encode and decode these skew cyclic codes.

The use of skew polynomial rings allows to endow linear codes with cyclic structures which are not cyclic in the classical (commutative) sense. Whenever these skew cyclic structures are carefully chosen, some control over the Hamming distance is gained, and it is possible to design efficient decoding algorithms. In this paper, we give a version of the Hartmann-Tzeng bound that works for a wide ...

In this paper we study a special type of linear codes, called skew cyclic codes, in the most general case. This set of codes is a generalization of cyclic codes but constructed using a non-commutative ring called the skew polynomial ring. In previous works these codes have been studied with certain restrictions on their length. This work examines their structure for an arbitrary length without ...

We design a non-commutative version of the Peterson-Gorenstein-Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In p...