Beyond the orthogonal array concept

Delsarte, Philippe
(2004) European Journal of Combinatorics — Vol. 25, n° 2, p. 187-198 (2004)

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  • Delsarte, PhilippeUCLouvain
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Abstract
Consider a block code Gamma of length n, over a q-ary alphabet. For a given integer t is an element of [0, n], the regularity of Gamma at level t is measured by the dimension of a well-defined subspace F of Rt+l, called the t-form space of the code. In particular, Gamma is an orthogonal array of strength t if and only if F = Rt+1. A central result of the paper is the close connection that exists between t-forms and T-designs in the Hamming scheme H(n, q). The t-form space F is shown to have the structure of an ideal, and the canonical generator of F to be computable from the distance distribution of the code Gamma. (C) 2003 Elsevier Ltd. All rights reserved.
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Delsarte, P. (2004). Beyond the orthogonal array concept. European Journal of Combinatorics, 25(2), 187-198. https://doi.org/10.1016/S0195-6698(03)00099-4 (Original work published 2004)