Binary codes derived from the Hoffman-Singleton and Higman-Sims graphs

Name: Binary codes derived from the Hoffman-Singleton and Higman-Sims graphs
Creator: Tonchev, Vladimir D.
Keywords: majority decoding, optimal linear code, Graphs and linear algebra (matrices, eigenvalues, etc.), automorphism group of a graph, strongly regular graph, weight distribution, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Linear codes (general theory)

Tonchev, Vladimir D.

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IEEE Transactions on Information Theory

Article . 1997 . Peer-reviewed

License: IEEE Copyright

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https://dx.doi.org/10.1109/18....

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Binary codes derived from the Hoffman-Singleton and Higman-Sims graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1997Publisher:Institute of Electrical and Electronics Engineers (IEEE)Journal:IEEE Transactions on Information Theory, volume 43, pages 1,021-1,025 (issn: 0018-9448,

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Authors: Tonchev, Vladimir D.;

doi: 10.1109/18.568714

Binary codes derived from the Hoffman-Singleton and Higman-Sims graphs

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Abstract

The author gives some binary linear codes of length 50 and 100 using the adjacency matrices of the Hoffman-Singleton graph and the Higman-Sims graph. Some of these codes are optimal or nearly optimal for the given length and dimension. The author also gives the weight distribution of the codes and observes that the dual codes admit majority logic decoding.

Related Organizations

Michigan Technological University
United States

Keywords

majority decoding, optimal linear code, Graphs and linear algebra (matrices, eigenvalues, etc.), automorphism group of a graph, strongly regular graph, weight distribution, Linear codes (general theory)

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