Refia Aksoy

• PhD
• Istanbul University

In the current paper, we study skew cyclic codes over the ring \({\mathcal {S}}:={\mathbb {F}}_2 \times ({\mathbb {F}}_2+v{\mathbb {F}}_2)\) with \(v^2=v\). We investigate the structural properties of skew cyclic codes over the ring \({\mathcal {S}}\). Also, we describe the dual codes of skew cyclic codes with respect to the Euclidean inner product...

In this paper, we study cyclic codes over the ring Fp×(Fp+vFp)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {F}_{p} \times (\mathbb {F}_{p}+v\mathbb {F}_{p})$\...

In the present study, we define cyclic codes over the commutative principal ideal ring F2 ? (F2 + vF2) with v2 = v and obtain some results on cyclic codes over F2 ? (F2 + vF2). We also investigate the dual of a cyclic code over F2 ? (F2 + vF2) depending on two inner products. We determine a generator polynomial of cyclic codes and give the calculat...

The original version of this article unfortunately contained some mistakes on the equations at page 4 of the published paper.

In this study we consider Euclidean and Hermitian self-dual codes over the direct product ring \(\mathbb {F}_{2} \times (\mathbb {F}_{2}+v\mathbb {F}_{2})\) where v2 = v. We obtain some theoretical outcomes about self-dual codes via the generator matrices of free linear codes over \(\mathbb {F}_{2} \times (\mathbb {F}_{2}+v\mathbb {F}_{2})\). Also,...

In this paper, free Euclidean self-dual codes over the ring F2 + v F2 with v2 =v of order 4 are considered. A necessary and sufficient condition for the form of the generator matrix of a free Euclidean self-dual code is given. By using the distance preserving Gray map from F2 + v F2 to F2 x F2, the generator matrix of the binary code which correspo...

In this paper, we investigate free Hermitian self-dual codes whose generator matrices are of the form [I,A+vB] over the ring F2+vF2={0,1,v,1+v} with v2=v. We use the double-circulant, the bordered double-circulant and the symmetric construction methods to obtain free Hermitian self-dual codes of even length. By describing a new shortening method ov...

In this work, we study linear codes over the ring \(\mathbb {F}_2 \times (\mathbb {F}_2+v\mathbb {F}_2)\) and their weight enumerators, where \(v^2=v\). We first give the structure of the ring and investigate linear codes over this ring. We also define two weights called Lee weight and Gray weight for these codes. Then we introduce two Gray maps fr...

In this paper, we give a method to lift binary self-dual codes to the ring . The lifting method requires solving a system of linear equations over . This technique is applied to binary self-dual code to obtain self-dual codes over . As Gray images of these codes, a substantial number of self-dual codes are generated. By using the extension theorem...