Higher Weights of Affine Grassmann Codes and Their Duals

TL;DR

This paper investigates the higher weights of affine Grassmann codes and their duals, providing explicit calculations and formulas, including a new proof for the dual code's minimum distance.

Contribution

It offers explicit determination of many higher weights for affine Grassmann codes and their duals, along with a simplified proof of a known minimum distance formula.

Findings

Explicit higher weights for affine Grassmann codes

Formulas for initial and terminal higher weights of dual codes

Simplified proof of the dual code's minimum distance

Abstract

We consider the question of determining the higher weights or the generalized Hamming weights of affine Grassmann codes and their duals. Several initial as well as terminal higher weights of affine Grassmann codes of an arbitrary level are determined explicitly. In the case of duals of these codes, we give a formula for many initial as well as terminal higher weights. As a special case, we obtain an alternative simpler proof of the formula of Beelen et al for the minimum distance of the dual of an affine Grasmann code.