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Cubic and higher degree bounds for codes and (t, m, s)-nets

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Abstract

The Plotkin bound and the quadratic bound for codes and (t, m, s)-nets can be obtained from the linear programming bound using certain linear and quadratic polynomials, respectively. We extend this approach by considering cubic and higher degree polynomials to find new explicit bounds as well as new non-existence results for codes and (t, m, s)-nets.

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Authors and Affiliations

  1. Department of Mathematics, University of Salzburg, Hellbrunnerstraße 34, 5020, Salzburg, Austria

    Horst Trinker

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  1. Horst Trinker
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Correspondence to Horst Trinker.

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Communicated by Juergen Bierbrauer.

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Trinker, H. Cubic and higher degree bounds for codes and (t, m, s)-nets. Des. Codes Cryptogr. 60, 101–121 (2011). https://doi.org/10.1007/s10623-010-9420-x

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  • DOI: https://doi.org/10.1007/s10623-010-9420-x

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