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Optimal Formally Self-Dual Codes over ?5 and ?7

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

In this paper, we study optimal formally self-dual codes over ?5 and ?7. We determine the highest possible minimum weight for such codes up to length 24. We also construct formally self-dual codes with highest minimum weight, some of which have the highest minimum weight among all known linear codes of corresponding length and dimension. In particular, the first known [14, 7, 7] code over ?7 is presented. We show that there exist formally self-dual codes which have higher minimum weights than any comparable self-dual codes.

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Authors and Affiliations

  1. Department of Mathematics, University of Scranton, Scranton, PA 18510, USA, , , , , , US

    Steven T. Dougherty

  2. Department of Electrical and Computer Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, Canada, V8W 3P6, , , , , , CA

    T. Aaron Gulliver

  3. Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan, , , , , , JP

    Masaaki Harada

Authors
  1. Steven T. Dougherty
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  2. T. Aaron Gulliver
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  3. Masaaki Harada
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Received: May 18, 1998; revised version: September 4, 1999

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Dougherty, S., Gulliver, T. & Harada, M. Optimal Formally Self-Dual Codes over ?5 and ?7 . AAECC 10, 227–236 (2000). https://doi.org/10.1007/s002000050126

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  • DOI: https://doi.org/10.1007/s002000050126

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