Revisiting the Weight Spectrum of the Affine Grassmann Code $C^{\mathbb{A}}(2,m)$

Rohit Yadav

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arXiv · 2609.10274

Revisiting the Weight Spectrum of the Affine Grassmann Code $C^{\mathbb{A}}(2,m)$

Rohit Yadav

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Abstract

Affine Grassmann codes, introduced by Beelen, Ghorpade and H{\o}holdt, are linear codes over $\mathbb{F}_q$ obtained by evaluating linear combinations of minors of a generic matrix. The weight spectrum of the affine Grassmann code $C^{\mathbb{A}}(2,m)$ was determined by Pi\~nero and Singh via a case analysis on the rank of an associated alternating matrix. We give an independent and more streamlined derivation, valid for all $m\ge4$ and every prime power $q$, in which each codeword is written in a compact matrix form and its Hamming weight is expressed through a single closed formula involving two explicit affine subspaces and their intersection.

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Rohit Yadav. 2026-09-09. Revisiting the Weight Spectrum of the Affine Grassmann Code $C^{\mathbb{A}}(2,m)$. https://arxiv.org/abs/2609.10274

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