Cyclic codes over some special rings

TL;DR

This paper investigates the structure and properties of cyclic codes over specific types of rings, including polynomial quotient rings and multivariate polynomial rings, expanding coding theory in algebraic structures.

Contribution

It introduces new classes of cyclic codes over special rings, analyzing their algebraic properties and potential applications in coding theory.

Findings

Characterization of cyclic codes over polynomial quotient rings.

Analysis of algebraic structure of codes over multivariate polynomial rings.

Potential applications in error correction and data transmission.

Abstract

In this paper we will study cyclic codes over some special rings: F_{q}[u]/(u^{i}), F_{q}[u_1,...u_{i}]/(u_1^2,u_2^2,...,u_{i}^2, u_1 u_2 - u_2 u_1,...,u_{i}u_{j} - u_{j}u_{i},...), F_{q}[u,v]/(u^{i},v^{j},uv-vu), q=p^{r}, where p is a prime number, r\in N-{0} and F_{q} is a field with q elements.