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Higher Weights for Ternary and Quaternary Self-Dual Codes*

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Abstract

We study higher weights applied to ternary and quaternary self-dual codes. We give lower bounds on the second higher weight and compute the second higher weights for optimal codes of length less than 24. We relate the joint weight enumerator with the higher weight enumerator and use this relationship to produce Gleason theorems. Graded rings of the higher weight enumerators are also determined.

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Authors and Affiliations

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

    Steven T. Dougherty

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

    T. Aaron. Gulliver

  3. Division of Mathematics, Sapporo Medical University, Sapporo, 060-8556, Japan

    Manabu Oura

Authors
  1. Steven T. Dougherty
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  2. T. Aaron. Gulliver
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  3. Manabu Oura
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Corresponding author

Correspondence to Steven T. Dougherty.

Additional information

Communicated by: J. D. Key

This work was supported in part by Northern Advancement Center for Science & Technology and the Natural Sciences and Engineering Research Council of Canada.

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Dougherty, S.T., Gulliver, T.A. & Oura, M. Higher Weights for Ternary and Quaternary Self-Dual Codes*. Des Codes Crypt 38, 97–112 (2006). https://doi.org/10.1007/s10623-004-5663-8

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  • DOI: https://doi.org/10.1007/s10623-004-5663-8

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