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.
Partially funded by “Agencia Española de Cooperación Internacional”, Project A/016959/08.
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Borges-Quintana, M., Borges-Trenard, M.A., Martínez-Moro, E. (2009). Gröbner Representations of Binary Matroids. In: Bras-Amorós, M., Høholdt, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2009. Lecture Notes in Computer Science, vol 5527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02181-7_26
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DOI: https://doi.org/10.1007/978-3-642-02181-7_26
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