LCD codes from adjacency matrices of graphs
| Autor: | Bernardo Gabriel Rodrigues, Jennifer D. Key |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Strongly regular graph Algebra and Number Theory Applied Mathematics Two-graph 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences Combinatorics Indifference graph 010201 computation theory & mathematics Chordal graph 0202 electrical engineering electronic engineering information engineering Adjacency list Cograph Adjacency matrix Graph product MathematicsofComputing_DISCRETEMATHEMATICS Mathematics |
| Zdroj: | Applicable Algebra in Engineering, Communication and Computing. 29:227-244 |
| ISSN: | 1432-0622 0938-1279 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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