Original scientific paper

Linear codes with complementary duals from some strongly regular subgraphs of the McLaughlin graph

Dimitri Leemans ; University of Auckland, Department of Mathematics, Private Bag 92 019, Auckland, New Zealand
Bernardo Rodrigues ; School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4 041, South Africa

Abstract

We describe a number of properties of some ternary linearcodes defined by the adjacency matrices of some stronglyregular graphs that occur as induced subgraphs of the McLaughlin graph, namely the graphs withparameters $(105,72,51,45), (120,77,52,44), (176, 105, 68, 54),$ and$(253, 140, 87, 65)$ respectively. We show that the codes withparameters $[120,21,30]_3$,$[120,99,6]_3$, $[176, 21, 56]_3$, $[176, 155, 6]_3$, $[253, 22, 97]_3$ and $[253, 231, 8]_3$ obtained from these graphs are linear codes with complementary duals and thus meet the asymptotic Gilbert–Varshamov bound.

Keywords

linear codes; strongly regular graphs; symmetric designs; automorphism groups

Hrčak ID:

170387

URI

https://hrcak.srce.hr/170387

Publication date:

11.11.2016.

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