Abstract
It has been widely known that complete decoding for binary linearcodes can be regarded as a linear integer programming problem with binary arithmetic conditions. Conti and Traverso [9] have proposed an algorithm whichuses Gröbner bases to solve integer programming with ordinary integer arithmeticconditions. Ikegami and Kaji [12] extended the Conti-Traverso algorithmto solve integer programming with modulo arithmetic conditions. It is natural toconsider for those problems the Graver basis associated to them which turns out tobe the minimal cycles of the matroid associated to the code, i.e. minimal supportcodewords in the binary case and its geometry. This provides us a universal test set for the programs considered.
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