Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6

被引：12

作者：

Heinlein, Daniel ^{[1
]}

Honold, Thomas ^{[2
]}

Kiermaier, Michael ^{[1
]}

Kurz, Sascha ^{[1
]}

Wassermann, Alfred ^{[1
]}

机构：

[1] Univ Bayreuth, Dept Math, Bayreuth, Germany

[2] Zhejiang Univ, ZJU UIUC Inst, Haining, Peoples R China

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2019年 / 87卷 / 2-3期

基金：

中国国家自然科学基金;

关键词：

Network coding; Constant-dimension codes; Subspace distance; Classification; Integer linear programming; ERROR-CORRECTING CODES; PROJECTIVE SPACES; BOUNDS;

D O I：

10.1007/s10623-018-0544-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We determine the maximum size A2(8,6;4) of a binary subspace code of packet length v=8, minimum subspace distance d=6, and constant dimension k=4 to be 257. There are two isomorphism types of optimal codes. Both of them are extended LMRD codes. In finite geometry terms, the maximum number of solids in PG(7,2) mutually intersecting in at most a point is 257. The result was obtained by combining the classification of substructures with integer linear programming techniques. This result implies that the maximum size A2(8,6) of a binary mixed-dimension subspace code of packet length 8 and minimum subspace distance6 is 257 as well.

引用

页码：375 / 391

页数：17

共 27 条

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