Handbook of Coding Theory
The Horace Method for Error-Correcting Codes: Mathematics Subject Classification (2000)
Applicable Algebra in Engineering, Communication and Computing
Lower bounds on minimal distance of evaluation codes
Applicable Algebra in Engineering, Communication and Computing
A symbolic test for (i,j)-uniformity in reduced zero-dimensional schemes
Journal of Symbolic Computation
Minimal vectors in linear codes
IEEE Transactions on Information Theory
Hardness of approximating the minimum distance of a linear code
IEEE Transactions on Information Theory
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If C is an [n,k,d]-linear code, computing its minimum distance, d, leads to deciding if certain ideals I generated by products of linear forms are Artinian or not (De Boer and Pellikaan, 1999). In this note we show that when these ideals are Artinian, then they must be powers of the maximal (irrelevant) ideal. We discuss some theoretical consequences of this result in connection to projective minimal codewords. In the end we compare the De Boer-Pellikaan method with the Migliore-Peterson method (Migliore and Peterson, 2004).