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On the minimal support codewords of linear codes over GF(q) and a note about IP equivalence classes
Intervenant(s) : Marta Conde (Spanish National Research Council)The knowledge of minimal support codewords is related to the complete decoding problem, which is NP: we generalise the upper bound for the number of minimal support codewords on binary codes constructed in [A. Alamadhi, R.E.L. Aldred, R. de la Cruz, P. Solé, C. Thomassen, "The maximum number of minimal codewords in long codes"] for codes over GF(q) and compare the behaviour of this bound with respect to the trivial one.
Separately, we characterize, via a complete system of invariants, the equivalence classes induced by the left action of the affine group GA(n,F) on the set of quadratic polynomial maps in F[x_1,...,x_n]^n with linear part of maximum rank.
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