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Directed strongly regular graphs and their codes
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The rank over a finite field of the adjacency matrix of a directed strongly regular graph is studied, with some applications to the construction of linear codes. Three techniques are used: code orthogonality, adjacency matrix determinant, and adjacency matrix spectrum.
Abstract
The rank over a finite field of the adjacency matrix of a directed strongly regular graph is studied, with some applications to the construction of linear codes. Three techniques are used: code orthogonality, adjacency matrix determinant, and adjacency matrix spectrum.
참고문헌 (10)
- E. F. Assmus, "Designs and their Codes" (1994)
- A. E. Brouwer, "On the p-rank of the adjacency matrices of strongly regular graphs", J. Algebraic Combin, 1(4), pp.329~346 (1992)
- A. E. Brouwer, "Spectra of Graphs" (2012), Springer
- A. M. Duval, "A directed graph version of strongly regular graphs", J. Comb. Th. Ser. A, 47(1), pp.71~100 (1988)
- C. D. Godsil, "Representations of directed strongly regular graphs", European J. Combin, 28(7), pp.1980~1993 (2007)
- W. H. Haemers, "Binary codes of strongly regular graphs", Des. Codes and Cryptography, 17(1-3), pp.187~209 (1999)
- W. C. Huffman, "Fundamentals of Error Correcting Codes" (2003)
- J.-L. Kim, "Skew Hadamard designs and their codes", Des. Codes and Cryptography, 49(1-3), pp.135~145 (2008)
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