The second minimum weight of Grassmann codes

2025/08/26 by Mrinmoy Datta, Datta, Mrinmoy, Tiasa Dutta +1 · 1 citation
Computer Science · Mathematics · #14G50 #14M15 #94B27 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #math.CO #math.IT #msc:14G50 #msc:14M15 #msc:94B27

paper · pdf · doi:10.48550/arxiv.2508.18844

arxiv created 2026/07/30 · arxiv updated 2026/07/31

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.

Citations

• Automorphism groups of Grassmann codes
• Weight spectrum of codes associated with the Grassmannian G(3,7)

Cited by

• On minimal codes arising from projective embeddings of point-line geometries

Related

• Higher weights of Grassmann codes in terms of properties of Schubert unions
• Grassmannian Codes as Lifts of Matrix Codes Derived as Images of Linear Block Codes over Finite Fields
• On the minimum distance of elliptic curve codes
• On the distance between linear codes
• A note on a gap in the proof of the minimum distance for Projective Reed-Muller Codes