IJPAM: Volume 70, No. 3 (2011)

A NOTE ON MATROIDS, CODES AND
INFORMATION THEORY

G.G. La Guardia$^1$, L. Grossi$^2$, R.C.A. Vieira$^3$, M.A.V. Pinto$^4$
$^{1,2,3}$Department of Mathematics and Statistics
State University of Ponta Grossa
84030-900, Ponta Grossa, PR, BRAZIL
$^4$Department of Mechanics Engineering
Federal University of Paraná
CP 19.011, 81.531-990, Curitiba, PR, BRAZIL


Abstract. In this note we show that the height function of a lattice of flats of suitable classes of matroids satisfies the polymatroidal axioms. Moreover, we present a novel proof, by applying matroid theory, for the fact that the minimum distance of a graph-theoretic code $C$ is the smallest number of edges among the edge sets of cycles of $G$, where $G$ is the graph arising $C$.

Received: November 24, 2010

AMS Subject Classification: 81Q99

Key Words and Phrases: matroid theory, error-correcting codes, information theory

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 3