Designs and their codes
On the p-Rank of the Adjacency Matrices of Strongly Regular Graphs
Journal of Algebraic Combinatorics: An International Journal
The Gewirtz graph: an exercise in the theory of graph spectra
European Journal of Combinatorics - Special issue: association schemes
Three new distance-regular graphs
European Journal of Combinatorics - Special issue: association schemes
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Binary Codes of Strongly Regular Graphs
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Permutation decoding for the binary codes from triangular graphs
European Journal of Combinatorics
A rank six geometry related to the McLaughlin sporadic simple group
Designs, Codes and Cryptography
Binary codes derived from the Hoffman-Singleton and Higman-Sims graphs
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
The article examines binary codes obtained from the row span of the adjacency matrices of some strongly regular graphs that occur as induced subgraphs of the McLaughlin graph, namely those with parameters (105, 32, 4, 12), (120, 42, 8, 18) and (253, 112, 36, 60). In addition we determine some primitive designs that are held by codewords of particular weights in the codes, and using the properties of the graphs and their geometry we provide a geometrical description of the nature of several classes of codewords. The codes with parameters [120, 100, 6]2 and [120, 101, 6]2 are near optimal as they are a distance 2 and 1 respectively more than the theoretical upper bound on the minimum distance for a code of the given length and dimension. Those with parameters [105, 87, 5]2 and [253, 231, 5]2 are a distance 1 less that the known recorded distance.