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The Weight Spectrum of the Affine Grassmann Code C𝔸(3,6)
Abstract
In this article, we consider the affine Grassmann code C𝔸(3,6), obtained from the affine open cell 𝔸9 of the Grassmannian G3,6. We exploit the representation of codewords as linear combinations of minors of all sizes of a generic 3×3 matrix and classify them according to the largest size of a minor occurring with a nonzero coefficient. Using this classification, we determine all possible Hamming weights of codewords of C𝔸(3,6) and, for each weight, compute the number of codewords attaining that weight. Consequently, we obtain the complete weight spectrum of the affine Grassmann code C𝔸(3,6).
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BibTeX
@misc{singh2026weight,
title = {{The Weight Spectrum of the Affine Grassmann Code $C^\mathbb A(3,6)$}},
author = {Prasant Singh and Rohit Yadav},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.08784},
eprint = {2609.08784},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08784},
}
RIS
TY - UNPB
TI - The Weight Spectrum of the Affine Grassmann Code C^𝔸(3,6)
AU - Prasant Singh
AU - Rohit Yadav
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2609.08784
UR - https://arxiv.org/abs/2609.08784
AB - In this article, we consider the affine Grassmann code C^𝔸(3,6), obtained from the affine open cell 𝔸^9 of the Grassmannian G_3,6. We exploit the representation of codewords as linear combinations of minors of all sizes of a generic 3×3 matrix and classify them according to the largest size of a minor occurring with a nonzero coefficient. Using this classification, we determine all possible Hamming weights of codewords of C^𝔸(3,6) and, for each weight, compute the number of codewords attaining that weight. Consequently, we obtain the complete weight spectrum of the affine Grassmann code C^𝔸(3,6).
ER -