Several families of ternary negacyclic codes and their duals

TL;DR

This paper constructs and analyzes several families of ternary negacyclic codes and their duals, highlighting their optimal distance properties and algebraic structures, which are less studied compared to cyclic codes.

Contribution

It introduces new families of ternary negacyclic codes and their duals with optimal distance properties, expanding the understanding of negacyclic code structures.

Findings

Contains distance-optimal codes

Exhibits good algebraic parameters

Expands knowledge on negacyclic codes

Abstract

Constacyclic codes contain cyclic codes as a subclass and have nice algebraic structures. Constacyclic codes have theoretical importance, as they are connected to a number of areas of mathematics and outperform cyclic codes in several aspects. Negacyclic codes are a subclass of constacyclic codes and are distance-optimal in many cases. However, compared with the extensive study of cyclic codes, negacyclic codes are much less studied. In this paper, several families of ternary negacyclic codes and their duals are constructed and analysed. These families of negacyclic codes and their duals contain distance-optimal codes and have very good parameters in general.