A geometric non-existence proof of an extremal additive code

作者：Bierbrauer Juergen^*; Marcugini Stefano; Pambianco Fernanda

来源：Journal of Combinatorial Theory - Series A, 2010, 117(2): 128-137.

DOI：10.1016/j.jcta.2009.04.005

• Additive codes
• Projective geometry
• Hyperplane
• Secundum
• Minimum distance
• Weight
• Strength
• Spread

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 coding-theoretic terms this is equivalent with the non-existence of an additive quaternary code of length 12, binary dimension 9 and minimum distance 7.

• 出版日期2010-2