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Self-orthogonal codes from the strongly regular graphs on up to 40 vertices (CROSBI ID 244417)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Crnković, Dean ; Maksimović, Marija ; Rodrigues, Bernardo Gabriel ; Rukavina, Sanja Self-orthogonal codes from the strongly regular graphs on up to 40 vertices // Advances in mathematics of communications, 10 (2016), 3; 555-582. doi: 10.3934/amc.2016026

Podaci o odgovornosti

Crnković, Dean ; Maksimović, Marija ; Rodrigues, Bernardo Gabriel ; Rukavina, Sanja

engleski

Self-orthogonal codes from the strongly regular graphs on up to 40 vertices

This paper outlines a method for constructing self-orthogonal codes from orbit matrices of strongly regular graphs admitting an automorphism group G which acts with orbits of length w, where w divides |G|. We apply this method to construct self-orthogonal codes from orbit matrices of the strongly regular graphs with at most 40 vertices. In particular, we construct codes from adjacency or orbit matrices of graphs with parameters (36, 15, 6, 6), (36, 14, 4, 6), (35, 16, 6, 8) and their complements, and from the graphs with parameters (40, 12, 2, 4) and their complements. That completes the classification of self-orthogonal codes spanned by the adjacency matrices or orbit matrices of the strongly regular graphs with at most 40 vertices. Furthermore, we construct ternary codes of 2-(27, 9, 4) designs obtained as residual designs of the symmetric (40, 13, 4) designs (complementary designs of the symmetric(40, 27, 18) designs), and their ternary hulls. Some of the obtained codes are optimal, and some are best known for the given length and dimension.

Strongly regular graph ; block design ; code ; orbit matrix

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Podaci o izdanju

10 (3)

2016.

555-582

objavljeno

1930-5346

1930-5338

10.3934/amc.2016026

Povezanost rada

Matematika

Poveznice
Indeksiranost