$(1-2u^2)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p$

TL;DR

This paper explores a specific class of constacyclic codes over a finite ring, detailing their generator polynomials and structural properties through a decomposition theorem, advancing algebraic coding theory.

Contribution

It introduces the structure and generator polynomials of $(1-2u^2)$-constacyclic codes over a particular ring, providing new insights into their algebraic properties.

Findings

Explicit description of generator polynomials

Decomposition theorem for structural analysis

Characterization of code properties

Abstract

Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^2)$-constacyclic codes over the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p$, where $u^3=u$. We describe generator polynomials of this kind of codes and investigate the structural properties of these codes by a decomposition theorem.