Linear codes with complementary duals from some strongly regular subgraphs of the McLaughlin graph
Leemans, Dimitri ; Rodrigues, Bernardo
Mathematical Communications, Tome 21 (2016) no. 1, p. 239-249 / Harvested from Mathematical Communications
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.
Publié le : 2016-06-26
Classification:  linear codes, strongly regular graphs, symmetric designs, automorphism groups,  05B05, 20D45, 94B05
@article{mc1537,
     author = {Leemans, Dimitri and Rodrigues, Bernardo},
     title = {Linear codes with complementary duals from some strongly regular subgraphs of the McLaughlin graph},
     journal = {Mathematical Communications},
     volume = {21},
     number = {1},
     year = {2016},
     pages = { 239-249},
     language = {eng},
     url = {http://dml.mathdoc.fr/item/mc1537}
}
Leemans, Dimitri; Rodrigues, Bernardo. Linear codes with complementary duals from some strongly regular subgraphs of the McLaughlin graph. Mathematical Communications, Tome 21 (2016) no. 1, pp.  239-249. http://gdmltest.u-ga.fr/item/mc1537/