The asymptotic number of inequivalent binary codes and nonisomorphic binary matroids
type: Item
instance of: scholarly article
title: The asymptotic number of inequivalent binary codes and nonisomorphic binary matroids
zbMATH Open document ID: 1006.94030
author: Marcel Wild
published in: Finite Fields and their Applications
publication date: 2002-01-06T00:00:00Z
review text: It is known that the number \(b(n)\) of inequivalent binary codes of length \(n\) gives the number of nonisomorphic binary \(n\)-matroids. The paper provides the asymptotic value of the number \(b(n)\) as \(n\to\infty\). Asymptotically, \(b(n)\equiv G(n)/n!\), where \(G(n)\) is the number of linear subspaces of \(\text{GF}(2)^n\).
Mathematics Subject Classification ID: 94B60
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 1471642
zbMATH Keywords: binary matroids
zbMATH Keywords: binary codes
reviewed by: Karl-Heinz Zimmermann
MaRDI profile type: Publication
full work available at URL: ffta.1999.0273
OpenAlex ID: W2075650493
cites work: The Invariant Subspace Lattice of a Linear Transformation
cites work: Q4220635
cites work: Gluings of modular lattices
cites work: Q5512461
cites work: Q5592270
cites work: Q3216750
cites work: Q4849839
cites work: Q4111952
cites work: Q3997906
cites work: Consequences of the Brylawski-Lucas theorem for binary matroids
cites work: Axiomatizing simple binary matroids by their closed circuits
DOI: 10.1006/FFTA.1999.0273
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description: scientific article; zbMATH DE number 1471642