Quasi-cyclic codes over a finite field are viewed as cyclic codes over a noncommutative ring of matrices over a finite field. This point of view permits to ...

Cyclic codes of length n over a finite field F are classified as the ideals ⟨ f ( x ) ⟩ of the quotient ring F [ x ] / ⟨ x n − 1 ⟩ , where f ( x ) is a divisor ...

Dec 3, 2009 · Quasi-cyclic codes are well-known and studied since the 60's. We can find, for example in [5] an introduc- tion to their applications, ...

Quasi-cyclic codes over a finite field are viewed as cyclic codes over a noncommutative ring of matrices over a finite field. This point of view permits to ...

We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary ...

The Lagrange interpolation polynomials in rings of matrices over finite fields are given and it is shown that they are maximum distance separable (MDS) and ...

This talk is based on joint work with San Ling (NTU, Singapore) on quasi cyclic codes. It is important to notice that, even if the.

Abstract. AbstractQuasi-cyclic codes over a finite field are viewed as cyclic codes over a noncommutative ring of matrices over a finite field.

Constacyclic codes have algebraic properties similar to cyclic codes [1, 20, 22]. For example they can also be specified through the roots of their generator ...

In this paper we study the fundamental algebraic properties (generation, duality) of cyclic codes over a special non-unitary ring without any polynomial ...