Symbol-pair Weight Distributions of Some Linear Codes

TL;DR

This paper studies the symbol-pair weight distributions of specific linear codes, revealing uniform weight properties in simplex codes and deriving distributions for variation simplex codes over finite fields.

Contribution

It provides new insights into symbol-pair weight distributions of MDS and simplex codes, including uniform weight properties and distributions for variation simplex codes.

Findings

All nonzero codewords of simplex codes have the same symbol b-weight.

Rearrangement of codewords can change symbol-pair weight.

Derived symbol b-weight distributions for variation simplex codes.

Abstract

In this paper, we investigate the symbol-pair weight distributions of MDS codes and simplex codes over finite fields. Furthermore, the result shows that all the nonzero codewords of simplex codes have the same symbol $b$-weight and rearrangement entries of codewords in simplex code may induce different symbol-pair weight. In addition, the symbol $b$-weight distributions of variation simplex codes over certain finite fields are derived.