Higher weights of Grassmann codes in terms of properties of Schubert unions

TL;DR

This paper characterizes the higher weights of Grassmann codes G(2,m) over finite fields using Schubert unions, providing explicit polynomial formulas for these weights.

Contribution

It introduces a novel approach linking Grassmann code weights to Schubert union properties and derives explicit polynomial formulas for these weights.

Findings

Higher weights of G(2,m) are expressed via Schubert unions.

Explicit polynomial formulas for weights are provided.

The method links algebraic geometry with coding theory.

Abstract

We describe the higher weights of the Grassmann codes $G(2,m)$ over finite fields ${\mathbb F}_q$ in terms of properties of Schubert unions, and in each case we determine the weight as the minimum of two explicit polynomial expressions in $q$.