Bounds on ordered codes and orthogonal arrays
Alexander Barg, Punarbasu Purkayastha
TL;DR
This paper provides new bounds on the size of codes and orthogonal arrays in the ordered Hamming space, and characterizes the eigenvalues of the associated scheme using multivariable Krawtchouk polynomials.
Contribution
It introduces novel estimates for code and array sizes in the ordered Hamming space and links the eigenvalues to multivariable Krawtchouk polynomials.
Findings
Derived new bounds for codes and orthogonal arrays in ordered Hamming space.
Identified eigenvalues of the ordered Hamming scheme as multivariable Krawtchouk polynomials.
Established properties of these polynomials within the scheme.
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 multivariable Krawtchouk polynomials, and establish some of their properties.
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Taxonomy
TopicsCoding theory and cryptography · Mathematical Approximation and Integration · graph theory and CDMA systems