Weight Distributions of Two Classes of Linear Codes with Five or Six Weights

TL;DR

This paper constructs and analyzes two classes of linear codes over finite fields with five or six weights, determining their weight distributions using Weil sums and exponential sums, and identifies some nearly optimal codes.

Contribution

It introduces new classes of linear codes with specific weight distributions and employs novel sum techniques to determine their properties, including near-optimal codes.

Findings

Constructed two classes of five- and six-weight linear codes over Fp.

Determined weight distributions using Weil sums and exponential sums.

Identified codes that are nearly optimal according to the Griesmer bound.

Abstract

In this paper, based on the theory of defining sets, two classes of five-weight or six-weight linear codes over Fp are constructed. The weight distributions of the linear codes are determined by means of Weil sums and a new type of exponential sums. In some case, there is an almost optimal code with respect to Griesmer bound, which is also an optimal one according to the online code table.