The FGLM Problem and Möller’s Algorithm on Zero-dimensional Ideals

Teo Mora ()
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Teo Mora: Università di Genova, DIMA and DISI

A chapter in Gröbner Bases, Coding, and Cryptography, 2009, pp 27-45 from Springer

Abstract: Abstract Möller’s Algorithm is a procedure which, given a set of linear functionals defining a zero-dimensional polynomial ideal, allows to compute, with good complexity, a set of polynomials which are triangular/bihortogonal to the given functionals; at least a “minimal” polynomial which vanishes to all the given functionals; a Gröbner basis of the given ideal. As such Möller’s Algorithm has applications when the functionals are point evaluation (where the only relevant informations are the bihortogonal polynomials); as an interpretation of Berlekamp–Massey Algorithm (such interpretation is due to Fitzpatrick) where the deduced minimal vanishing polynomial is the key equation; as an efficient solution of the FGLM-Problem (deduced with good complexity the lex Gröbner basis of a zero-dim. ideal given by another easy-to-be-computed Gröbner basis of the same ideal).

Keywords: Linear Code; Hilbert Function; Order Ideal; Binary Linear Code; Multivariate Interpolation (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-93806-4_3

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DOI: 10.1007/978-3-540-93806-4_3

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