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A simple derivation of the MacWilliams identity for linear ordered codes and orthogonal arrays

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Abstract

In (Can J Math 51(2):326–346, 1999), Martin and Stinson provide a generalized MacWilliams identity for linear ordered orthogonal arrays and linear ordered codes (introduced by Rosenbloom and Tsfasman (Prob Inform Transm 33(1):45–52, 1997) as “codes for the m-metric”) using association schemes. We give an elementary proof of this generalized MacWilliams identity using group characters and use it to derive an explicit formula for the dual type distribution of a linear ordered code or orthogonal array.

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  1. Department of Mathematics, University of Salzburg, Hellbrunnerstaße 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 J. Bierbrauer.

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Trinker, H. A simple derivation of the MacWilliams identity for linear ordered codes and orthogonal arrays. Des. Codes Cryptogr. 50, 229–234 (2009). https://doi.org/10.1007/s10623-008-9226-2

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  • DOI: https://doi.org/10.1007/s10623-008-9226-2

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