Gröbner Representations of Binary Matroids

Authors:
M. Borges-Quintana;M. A. Borges-Trenard;E. Martínez-Moro
Affiliations:
Dpto. de Matemática, FCMC, U. de Oriente, Santiago de Cuba, Cuba;Dpto. de Matemática, FCMC, U. de Oriente, Santiago de Cuba, Cuba;Dpto. de Matemática Aplicada, U. de Valladolid, Castilla, Spain
Venue:
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2009

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Abstract

Several constructions in binary linear block codes are also related to matroid theory topics. These constructions rely on a given order in the ground set of the matroid. In this paper we define the Gröbner representation of a binary matroid and we show how it can be used for studying different sets bases, cycles, activity intervals, etc.