Optimal binary subspace codes of length 6, constant dimension 3 and minimum subspace distance 4

被引：30

作者：

Honold, Thomas ^{[1
]}

Kiermaier, Michael ^{[2
]}

Kurz, Sascha ^{[2
]}

机构：

[1] Zhejiang Univ, Dept Informat & Elect Engn, Hangzhou 310027, Zhejiang, Peoples R China

[2] Univ Bayreuth, Math Inst, D-95440 Bayreuth, Germany

来源：

TOPICS IN FINITE FIELDS | 2015年 / 632卷

关键词：

Subspace code; network coding; partial spread; PARTIAL SPREADS; DESIGNS; SPACES;

D O I：

10.1090/conm/632/12627

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that the maximum size of a binary subspace code of packet length v = 6, minimum subspace distance d = 4, and constant dimension k = 3 is M = 77; in Finite Geometry terms, the maximum number of planes in PG(5, 2) mutually intersecting in at most a point is 77. Optimal binary (v, M, d; k) = (6, 77, 4; 3) subspace codes are classified into 5 isomorphism types, and a computer-free construction of one isomorphism type is provided. The construction uses both geometry and finite fields theory and generalizes to any q, yielding a new family of q-ary (6, q(6) 2q(2) 2q 1,4; 3) subspace codes.

引用

页码：157 / 176

页数：20

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