Bases of Cocycle Lattices and Submatrices of a Hadamard Matrix

Hochstättler, Winfried and Loebl, Martin (1999) Bases of Cocycle Lattices and Submatrices of a Hadamard Matrix.
Published In: Contemporary trends in discrete mathematics : from DIMACS and DIMATIA to the future ; DIMATIA-DIMACS conference, May 19 - 25, 1997, Štiřín Castle, Czech Republic ; [contains papers from a DIMATIA/DIMACS Conference on the Future of Discrete Mathematics], DIMACS series in discrete mathematics and theoretical computer science. 49 American Mathematical Society (AMS). 49 American Mathematical Society (AMS) 1999, pp. 159-168.

Abstract

We study the lattice lat(M) of cocycles of a binary matroid M. By an isomorphism we show that such lattices are equivalent to lattices generated by the columns of proper submatrices of Sylvester matrices of full row length. As an application we show that the cocycle lattice of a recursively defined class of matroids, including all binary matroids of rank four, always has a basis consisting of cocycles.


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Deposit Information:
ZAIK Number: zpr98-315
Depositing User: Winfried Hochstättler
Date Deposited: 02 Apr 2001 00:00
Last Modified: 19 Dec 2011 09:45
URI: http://e-archive.informatik.uni-koeln.de/id/eprint/315