Equivalence and Duality of Polycyclic Codes Associated with Trinomials over Finite Fields

TL;DR

This paper investigates the properties of polycyclic codes linked to trinomials over finite fields, focusing on their equivalence, duality, and methods for constructing special classes like isodual and self-dual codes.

Contribution

It introduces new methods for constructing isodual and self-dual polycyclic codes and explores their self-orthogonal and dual-containing properties over F2.

Findings

Methods to construct isodual and self-dual polycyclic codes.

Analysis of self-orthogonal and dual-containing polycyclic codes over F2.

Validation of several conjectures related to code equivalence and duality.

Abstract

In this paper, several conjectures proposed in [2] are studied, involving the equivalence and duality of polycyclic codes associated with trinomials. According to the results, we give methods to construct isodual and self-dual polycyclic codes, and study the self-orthogonal and dual-containing polycyclic codes over F2.