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Revisiting the Weight Spectrum of the Affine Grassmann Code C𝔸(2,m)
Abstract
Affine Grassmann codes, introduced by Beelen, Ghorpade and Høholdt, are linear codes over 𝔽q obtained by evaluating linear combinations of minors of a generic matrix. The weight spectrum of the affine Grassmann code C𝔸(2,m) was determined by Piñero 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≥4 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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BibTeX
@misc{yadav2026revisiting,
title = {{Revisiting the Weight Spectrum of the Affine Grassmann Code $C^\mathbbA(2,m)$}},
author = {Rohit Yadav},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10274},
eprint = {2609.10274},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10274},
}
RIS
TY - UNPB
TI - Revisiting the Weight Spectrum of the Affine Grassmann Code C^𝔸(2,m)
AU - Rohit Yadav
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10274
UR - https://arxiv.org/abs/2609.10274
AB - Affine Grassmann codes, introduced by Beelen, Ghorpade and Høholdt, are linear codes over 𝔽_q obtained by evaluating linear combinations of minors of a generic matrix. The weight spectrum of the affine Grassmann code C^𝔸(2,m) was determined by Piñero 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≥4 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.
ER -