Higher weights of Grassmann codes in terms of properties of Schubert unions

2011/04/30 by Sudhir R. Ghorpade, Trygve Johnsen, Ghorpade, Sudhir R. +5
Computer Science · Mathematics · #05E15 #14M15 #94B27 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #math.AG #math.CO #math.IT #msc:05E15 #msc:14M15 #msc:94B27

paper · pdf · doi:10.48550/arxiv.1105.0087

12 pages, 5 figures

arxiv created 2011/04/30 · arxiv updated 2011/05/04

Abstract

We describe the higher weights of the Grassmann codes G(2,m) over finite fields \mathbb F_q in terms of properties of Schubert unions, and in each case we determine the weight as the minimum of two explicit polynomial expressions in q.

Related

• Schubert Unions in Grassmann Varieties
• The structure of dual Schubert union codes
• The second minimum weight of Grassmann codes
• The second weight of generalized Reed-Muller codes in most cases
• Generalized Reed-Muller codes and curves with many points