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The existence of extremal self-dual [50,25,10] codes and quasi-symmetric 2-(49,9,6) designs

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Abstract

All extremal binary self-dual [50,25,10] codes with an automorphism of order 7 are enumerated. Up to equivalence, there are four such codes, three with full automorphism group of order 21, and one code with full group of order 7. The minimum weight codewords yield quasi-symmetric 2-(49,9,6) designs.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Loyola University, 60626, Chicago, Illinois

    W. Cary Huffman

  2. Department of Mathematical Sciences, Michigan Technological University, 49931, Houghton, Michigan

    Vladimir D. Tonchev

Authors
  1. W. Cary Huffman
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  2. Vladimir D. Tonchev
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Additional information

Communicated by: D. Jungnickel

Research supported in part by NSA grant MDA904-95-H-1019.

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Huffman, W.C., Tonchev, V.D. The existence of extremal self-dual [50,25,10] codes and quasi-symmetric 2-(49,9,6) designs. Des Codes Crypt 6, 97–106 (1995). https://doi.org/10.1007/BF01398008

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  • DOI: https://doi.org/10.1007/BF01398008

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