The graphs of projective codes

被引：6

作者：

Kwiatkowski, Mariusz ^{[1
]}

Pankov, Mark ^{[1
]}

Pasini, Antonio ^{[2
]}

机构：

[1] Univ Warmia & Mazury, Fac Math & Comp Sci, Sloneczna 54, Olsztyn, Poland

[2] Univ Siena, Dept Informat Engn & Math, Via Roma 56, Siena, Italy

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2018年 / 54卷

关键词：

Linear code; Projective code; Simplex code; Grassmann graph; LINEAR CODES;

D O I：

10.1016/j.ffa.2018.07.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider the Grassmann graph formed by k-dimensional subspaces of an n-dimensional vector space over the field of q elements (1 < k < n-1) and denote by II(n, k), the restriction of this graph to the set of projective [n, k](q) codes. In the case when q >= ((n)(2)), we show that the graph II(n, k)(q) is connected, its diameter is equal to the diameter of the Grassmann graph and the distance between any two vertices coincides with the distance between these vertices in the Grassmann graph. Also, we give some observations concerning the graphs of simplex codes. For example, binary simplex codes of dimension 3 are precisely maximal singular subspaces of a non-degenerate quadratic form. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：15 / 29

页数：15

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