We use a geometric approach to solve an extremal problem in coding theory. Expressed in geometric language we show the nonexistence of a system of 12 lines in PG(8, 2) with the property that no hyperplane contains more than 5 of the lines. In codingtheoretic terms this is equivalent with the non-existence of an additive quaternary code of length 12, binary dimension 9 and minimum distance 7.
A geometric non-existence proof of an extremal additive code
MARCUGINI, Stefano;PAMBIANCO, Fernanda
2010
Abstract
We use a geometric approach to solve an extremal problem in coding theory. Expressed in geometric language we show the nonexistence of a system of 12 lines in PG(8, 2) with the property that no hyperplane contains more than 5 of the lines. In codingtheoretic terms this is equivalent with the non-existence of an additive quaternary code of length 12, binary dimension 9 and minimum distance 7.File in questo prodotto:
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