Abstract Reed–Solomon codes and Gabidulin codes have maximum Hamming distance and
maximum rank distance, respectively. A general construction using skew polynomials, called …

In wireless network sharing information between source and receiving need is complex as
no wired communication channel. The wireless channel is subjected to many disturbances …

We propose a decoding algorithm for a class of convolutional codes called skew Reed-
Solomon convolutional codes. These are convolutional codes of designed Hamming …

We develop two algorithms for computing a bound of an Ore polynomial over a skew field,
under mild conditions. As an application, we state a criterion for deciding whether a …

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 …

In this paper, an application of the theoretical algebraic notion of a separable ring extension
in the realm of cyclic convolutional codes or, more generally, ideal codes, is investigated. It …

In this paper, a Roos like bound on the minimum distance for skew cyclic codes over a
general field is provided. The result holds in the Hamming metric and in the rank metric. The …

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 …

We consider the algorithmic problem of computing a primitive idempotent of a central simple
algebra over the field of rational functions over a finite field. The algebra is given by a set of …

We prove that any square nilpotent matrix over a field is a difference of two idempotent
matrices as well as that any square matrix over an algebraically closed field is a sum of a …