A characterization of some odd sets in projective spaces of order 4 and the extendability of quaternary linear codes

被引：3
|
作者：
Tanaka T. [1 ]
Maruta T. [1 ]
机构：
[1] Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Osaka
来源：
Journal of Geometry | 2014年 / 105卷 / 1期
基金：
日本学术振兴会;
关键词：
extensions; finite projective spaces; linear codes; Odd sets;
D O I：
10.1007/s00022-013-0195-x
中图分类号：
学科分类号：
摘要：
A set K in PG(r, 4), r ≥ 2, is odd if every line meets K in an odd number of points. An odd set K in PG(r, 4), r ≥ 3, is FH-free if there is no plane meeting K in a Fano plane or in a non-singular Hermitian curve. We prove that an odd set K contains a hyperplane of PG(r, 4) if and only if K is FH-free. As an application to coding theory, a new extension theorem for quaternary linear codes is given. © 2013 Springer Basel.
引用
收藏
页码：79 / 86
页数：7
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