Stanley-Reisner resolution of constant weight linear codes

TL;DR

This paper explores the algebraic and combinatorial properties of constant weight linear codes by analyzing their weight hierarchy and the Stanley-Reisner resolution of associated matroids, providing conditions to identify constant weight codes.

Contribution

It introduces new conditions on higher weights that guarantee a linear code is of constant weight, linking algebraic invariants to combinatorial properties.

Findings

Derived conditions on higher weights for constant weight codes

Analyzed the Stanley-Reisner resolution of associated matroids

Connected weight hierarchy with algebraic and combinatorial structures

Abstract

Given a constant weight linear code, we investigate its weight hierarchy and the Stanley-Reisner resolution of its associated matroid regarded as a simplicial complex. We also exhibit conditions on the higher weights sufficient to conclude that the code is of constant weight