On the Codes Related to the Higman-Sims Graph
نویسندگان
چکیده
منابع مشابه
Linear codes with complementary duals related to the complement of the Higman-Sims graph
In this paper we study codes $C_p(overline{{rm HiS}})$ where $p =3,7, 11$ defined by the 3- 7- and 11-modular representations of the simple sporadic group ${rm HS}$ of Higman and Sims of degree 100. With exception of $p=11$ the codes are those defined by the row span of the adjacency matrix of the complement of the Higman-Sims graph over $GF(3)$ and $GF(7).$ We show that these codes ha...
متن کاملOn the Codes Related to the Higman-Sims Graph
All linear codes of length 100 over a field F which admit the Higman-Sims simple group HS in its rank 3 representation are determined. By group representation theory it is proved that they can all be understood as submodules of the permutation module FΩ where Ω denotes the vertex set of the Higman-Sims graph. This module is semisimple if charF 6= 2, 5 and absolutely indecomposable otherwise. Al...
متن کاملDecomposing the Higman-Sims graph into double Petersen graphs
It has been known for some time that the Higman-Sims graph can be decomposed into the disjoint union of two Hoffman-Singleton graphs. In this paper we establish that the Higman-Sims graph can be edge decomposed into the disjoint union of 5 double-Petersen graphs, each on 20 vertices. It is shown that in fact this can be achieved in 36960 distinct ways. It is also shown that these different ways...
متن کاملOn the Graphs of Hoffman-Singleton and Higman-Sims
We propose a new elementary definition of the Higman-Sims graph in which the 100 vertices are parametrised with Z4 × Z5 × Z5 and adjacencies are described by linear and quadratic equations. This definition extends Robertson’s pentagonpentagram definition of the Hoffman-Singleton graph and is obtained by studying maximum cocliques of the Hoffman-Singleton graph in Robertson’s parametrisation. Th...
متن کاملTight Subdesigns of the Higman-sims Design
The Higman-Sims design is an incidence structure of 176 points and 176 blocks of cardinality 50 with every two blocks meeting in 14 points. The automorphism group of this design is the Higman-Sims simple group. We demonstrate that the point set and the block set of the Higman-Sims design can be partitioned into subsets X1, X2, . . . , X11 and B1, B2, . . . , B11, respectively, so that the subst...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/4267