A simple derivation of the MacWilliams identity for linear ordered codes and orthogonal arrays |
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Authors: | Horst Trinker |
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Affiliation: | 1.Department of Mathematics,University of Salzburg,Salzburg,Austria |
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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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Keywords: | Generalized MacWilliams identity Ordered codes and orthogonal arrays Generalized Krawtchouk polynomials Linear programming bound for (t, m, s)-nets |
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