Alexander Barg, Punabrasu Purkayastha, “Bounds on ordered codes and orthogonal arrays”, Mosc. Math. J., 2009, Volume 9, Number 2,Pages <nobr>211

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Bounds on ordered codes and orthogonal arrays

Alexander Barg^ab, Punabrasu Purkayastha^b

^a Institute for Problems of Information Transmission, Russian Academy of Sciences, Moscow, Russia
^b Dept. of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA

Abstract: We derive new estimates of the size of codes and orthogonal arrays in the ordered Hamming space (the Niederreiter–Rosenbloom–Tsfasman space). We also show that the eigenvalues of the ordered Hamming scheme, the association scheme that describes the combinatorics of the space, are given by the multivariate Krawtchouk polynomials, and establish some of their properties.

Key words and phrases: ordered Hamming space, association schemes, multivariate Krawtchouk polynomials, Delsarte method, asymptotic bounds.

MSC: Primary 05E30; Secondary 94B65

Received: February 5, 2007

Language: English

DOI: 10.17323/1609-4514-2009-9-2-211-243