Details:
Title  Decomposition of modular codes for computing test sets and Graver basis.  Author(s)  Irene MárquezCorbella, Edgar MartinezMoro  Type  Article in Journal  Abstract  In order to obtain the set of codewords of minimal support for codes defined over ℤq, one can compute a Graver basis of the ideal associated to such codes. The main aim of this article is to reduce the complexity of the algorithm obtained by the authors in a previous work taking advantage of the powerful decomposition theory for linear codes provided by the decomposition theory of representable matroids over finite fields. In this way we identify the codes that can be written as “gluing” of codes of shorter length. If this decomposition verifies certain properties then computing the set of codewords of minimal support in each code appearing in the decomposition is equivalent to computing the set of codewords of minimal support for the original code. Moreover, these computations are independent of each other, thus they can be carried out in parallel for each component, thereby not only obtaining a reduction of the complexity of the algorithm but also decreasing the time needed to process it.  Keywords  Matroid theory, Code decompositions, Test sets, Universal test sets, Minimal support codewords, Gröbner basis  ISSN  16618270; 16618289/e 
URL 
http://link.springer.com/article/10.1007%2Fs117860120120y 
Language  English  Journal  Math. Comput. Sci.  Volume  6  Number  2  Pages  147165  Publisher  Springer (Birkh\"auser), Basel  Year  2012  Edition  0  Translation 
No  Refereed 
No 
