LCD codes from adjacency matrices of graphs

被引：0
作者：
J. D. Key
B. G. Rodrigues
机构：
[1] Aberystwyth University,Institute of Mathematics, Physics and Computer Science
[2] University of KwaZulu-Natal,School of Mathematics, Statistics and Computer Science
来源：
Applicable Algebra in Engineering, Communication and Computing | 2018年 / 29卷
关键词：
codes; Uniform subset graphs; Strongly regular graphs; 05C50; 94B05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
It is shown how LCD codes with a particularly useful feature can be found from row spans over finite fields of adjacency matrices of graphs by considering these together with the codes from the associated reflexive graphs and complementary graphs. Application is made to some particular classes, including uniform subset graphs and strongly regular graphs where, if a p-ary code from a graph has this special LCD feature, the dimension can be found from the multiplicities modulo p of the eigenvalues of an adjacency matrix and, bounds on the minimum weight of the code and the dual code follow from the valency of the graph.
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页码：227 / 244
页数：17
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