Barg, Alexander; Purkayastha, Punarbasu Bounds on ordered codes and orthogonal arrays. (English) Zbl 1220.05135 Mosc. Math. J. 9, No. 2, 211-243 (2009). Summary: 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. Cited in 7 Documents MSC: 05E30 Association schemes, strongly regular graphs 94B65 Bounds on codes Keywords:ordered Hamming space; association schemes; multivariate Krawtchouk polynomials; Delsarte method; asymptotic bounds PDFBibTeX XMLCite \textit{A. Barg} and \textit{P. Purkayastha}, Mosc. Math. J. 9, No. 2, 211--243 (2009; Zbl 1220.05135) Full Text: arXiv Link