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Weight Enumerators of Double Circulant Codes and New Extremal Self-Dual Codes

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Abstract

In this paper it is shown that the weight enumerator of a bordered double circulant self-dual code can be obtained from those of a pure double circulant self-dual code and its shadow through a relationship between bordered and pure double circulant codes. As applications, a restriction on the weight enumerators of some extremal double circulant codes is determined and a uniqueness proof of extremal double circulant self-dual codes of length 46 is given. New extremal singly-even [44,22,8] double circulant codes are constructed. These codes have weight enumerators for which extremal codes were not previously known to exist.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    T. Aaron Gulliver

  2. Department of Mathematics, Okayama University, Okayama, 700, Japan

    Masaaki Harada

Authors
  1. T. Aaron Gulliver
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  2. Masaaki Harada
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Gulliver, T.A., Harada, M. Weight Enumerators of Double Circulant Codes and New Extremal Self-Dual Codes. Designs, Codes and Cryptography 11, 141–150 (1997). https://doi.org/10.1023/A:1008276604233

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