论文信息 - An Application of Möller's Algorithm to Coding Theory

An Application of Möller's Algorithm to Coding Theory

We show the use of Moller’s Algorithm and related techniques for decoding and studying some combinatorial properties of linear codes. It is a concise summary of our previous results, with emphasis in illustrating the applications and comparing the developed method for computing the Grobner basis associated with the code with the classical way to solve the same problem.

Edgar Martínez-Moro | Mijail Borges-Quintana | Miguel A. Borges-Trenard

[1] Teo Mora. The FGLM Problem and Möller's Algorithm on Zero-dimensional Ideals , 2009, Gröbner Bases, Coding, and Cryptography.

[2] Bruno Buchberger,et al. Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal , 2006, J. Symb. Comput..

[3] Edgar Martínez-Moro,et al. Gröbner bases and combinatorics for binary codes , 2008, Applicable Algebra in Engineering, Communication and Computing.

[4] Edgar Martínez-Moro,et al. A General Framework for Applying FGLM Techniques to Linear Codes , 2006, AAECC.

[5] Maria Grazia Marinari,et al. Gröbner bases of ideals defined by functionals with an application to ideals of projective points , 1993, Applicable Algebra in Engineering, Communication and Computing.

[6] Teo Mora,et al. Computing Gröbner Bases by FGLM Techniques in a Non-commutative Setting , 2000, J. Symb. Comput..

[7] M. Borges-Quintana,et al. On a Gröbner bases structure associated to linear codes , 2005 .

[8] Jean-Charles Faugère,et al. Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering , 1993, J. Symb. Comput..