Complete Weight Enumerator of a Family of Linear Codes from Cyclotomy

TL;DR

This paper derives explicit formulas for the complete weight enumerators of a family of linear codes constructed from cyclotomy, which are relevant for cryptography and secret sharing.

Contribution

It provides the first explicit determination of complete weight enumerators for these codes based on cyclotomy, expanding understanding of their structure.

Findings

Explicit formulas for complete weight enumerators are derived.

Codes have potential applications in cryptography and secret sharing.

The work advances the theoretical understanding of cyclotomic-based codes.

Abstract

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for a prime $p$, we determine the explicit complete weight enumerators of a family of linear codes over $\mathbb{F}_p$ with defining set related to cyclotomy. These codes may have applications in cryptography and secret sharing schemes.