The weight distributions of some linear codes derived from Kloosterman sums

TL;DR

This paper constructs specific p-ary linear codes with few weights using Kloosterman sums over finite fields, determining their weight distributions and identifying some as minimal codes, which are useful in data security applications.

Contribution

It introduces new p-ary linear codes derived from Kloosterman sums and explicitly determines their weight distributions, including minimal codes, advancing coding theory.

Findings

Constructed new linear codes with few weights

Determined weight distributions using Kloosterman sums

Identified some codes as minimal codes

Abstract

Linear codes with few weights have applications in data storage systems, secret sharing schemes, and authentication codes. In this paper, some kinds of p-ary linear codes with few weights are constructed by use of the given de ning set, where p is a prime. Their weight distributions are determined based on Kloosterman sums over nite elds. In addition, some linear codes we given is minimal.