A geometric non-existence proof of an extremal additive code

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:117

Article

Bierbrauer, Juergen¹  Marcugini, Stefano²  Pambianco, Fernanda² 

[1] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

[2] Univ Perugia, Dipartimento Matemat & Informat, I-06100 Perugia, Italy

关键词: Additive codes;    Projective geometry;    Hyperplane;    Secundum;    Minimum distance;    Weight;    Strength;    Spread;   

DOI  :  10.1016/j.jcta.2009.04.005

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free