A Note on Small Weight Codewords of Projective Geometric Codes and on the Smallest Sets of Even Type
Sam Adriaensen
Source abstract
Abstract. In this paper, we study the codes [Formula: see text] arising from the incidence of points and [Formula: see text]-spaces in [Formula: see text] over the field [Formula: see text], with [Formula: see text], [Formula: see text] prime. We classify all codewords of minimum weight of the dual code [Formula: see text] in case [Formula: see text]. This is equivalent to classifying the smallest sets of even type in [Formula: see text] for [Formula: see text]. We also provide shorter proofs for some already known results, namely, of the best known lower bound on the minimum weight of [Formula: see text] for general values of [Formula: see text], and of the classification of all codewords of [Formula: see text] of weight up to [Formula: see text].
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