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Mosc. Math. J., 2002, Volume 2, Number 1, Pages 81–97 (Mi mmj46)  

This article is cited in 58 scientific papers (total in 58 papers)

MacWilliams duality and the Rosenbloom–Tsfasman metric

S. T. Doughertya, M. M. Skriganovb

a University of Scranton
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: 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.

Key words and phrases: Codes in the Rosenbloom–Tsfasman metric, MacWilliams relations, uniform distributions.


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MSC: 94B, 11K, 94A
Received: March 5, 2001; in revised form November 15, 2001

Citation: S. T. Dougherty, M. M. Skriganov, “MacWilliams duality and the Rosenbloom–Tsfasman metric”, Mosc. Math. J., 2:1 (2002), 81–97

Citation in format AMSBIB
\by S.~T.~Dougherty, M.~M.~Skriganov
\paper MacWilliams duality and the Rosenbloom--Tsfasman metric
\jour Mosc. Math.~J.
\yr 2002
\vol 2
\issue 1
\pages 81--97

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