Macwilliams Duality and the Rosenbloom–tsfasman Metric
نویسندگان
چکیده
A new non-Hamming metric on linear spaces over finite fields has recently been introduced by Rosenbloom and Tsfasman [8]. We consider orbits of linear groups preserving the metric and show that weight enumerators suitably associated with such orbits satisfy MacWilliams-type identities for mutually dual codes. Furthermore, we show that the corresponding weight spectra of dual codes are related by transformations which involve multi-dimensional generalizations of known Krawtchouk polynomials. The relationships with recent results by Godsil [5] and Martin and Stinson [7] on MacWilliams-type theorems for association schemes and ordered orthogonal arrays are also briefly discussed in the paper. 2000 Math. Subj. Class. 94B, 11K, 94A.
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