Algebraic Construction and Analysis of Double-Cyclic Codes over $\mathbb{Z}_{p}\bigoplus u\mathbb{Z}_{p}$

Document Type : Original Article

Authors

Zakariae Cheddour

Abdelhamid Tadmori

Department of Mathematics, University Abdelmalek Essaadi, Faculty of Sciences and Technology Al Hoceima, BP 34. Ajdir 32003 Al Hoceima, Morocco.

10.22034/kjm.2025.513627.3491

Abstract

This study explores the structure and properties of cyclic codes and extends the analysis to double cyclic codes over the ring $\Re = \mathbb{Z}_{p}\bigoplus u \mathbb{Z}_{p}$. The objective is to determine the generator polynomials for double cyclic codes. A systematic approach is developed for constructing these generator polynomials using algebraic techniques. Additionally, the research investigates the ranks and minimal covering sets associated with double cyclic codes.

Keywords

Linear code

cyclic codes

double-cyclic codes

Subjects

• 16 Associative rings and algebras

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