The second minimum weight of Grassmann codes
Mrinmoy Datta, Tiasa Dutta
TL;DR
This paper provides a combinatorial proof of Nogin's Theorem on the minimum distance of Grassmann codes and extends the method to determine the second minimum weight, enhancing understanding of these codes' error-correcting capabilities.
Contribution
It introduces a new combinatorial approach to analyze Grassmann codes and computes their second minimum weight, which was previously unknown.
Findings
Combinatorial proof of Nogin's Theorem
Calculation of the second minimum weight of Grassmann codes
Enhanced understanding of Grassmann codes' error correction
Abstract
We give an independent combinatorial proof of Nogin's Theorem concerning the minimum distance of the Grassmann codes using a special decomposition of the Grassmannians. We use the same idea to also compute the second minimum weight of the Grassmann codes.
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