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Optimal subcodes of formally self-dual codes and their optimum distance profiles

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Abstract

A (binary) formally self-dual code is a linear code whose weight enumerator is equal to that of its dual. Little is known about the existence of optimal subcodes of formally self-dual codes. In this paper we show that some optimal formally self-dual codes actually contain optimal subcodes by computing the optimum distance profiles (ODPs) of linear codes. We determine the ODPs of optimal formally self-dual codes with parameters \([16, 8, 5], [18, 9, 6], [20, 10, 6]\) and \([22,11,7]\) and show that they contain optimal subcodes with high minimum weights.

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Acknowledgments

J.-L. Kim would like to mention that this work was supported by the Sogang University Research Grant of 201210058.01.

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Authors and Affiliations

  1. Department of Mathematics, Ohio Dominican University, Columbus, OH, 43219, USA

    Finley Freibert

  2. Department of Mathematics, Sogang University, Seoul, 121-742, South Korea

    Jon-Lark Kim

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  1. Finley Freibert
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  2. Jon-Lark Kim
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Correspondence to Jon-Lark Kim.

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Freibert, F., Kim, JL. Optimal subcodes of formally self-dual codes and their optimum distance profiles. AAECC 24, 215–224 (2013). https://doi.org/10.1007/s00200-013-0195-y

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  • DOI: https://doi.org/10.1007/s00200-013-0195-y

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