Nonexistence of (17, 108, 3) ternary orthogonal array

TitleNonexistence of (17, 108, 3) ternary orthogonal array
Publication TypeJournal Article
Year of Publication2019
AuthorsBoumova S, Marinova T, Ramaj T, Stoyanova M
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Start Page117
ISSN1313-9215 (Print) 2603-5529 (Online)
Keywordsdistance distributions, Hamming space, Krawtchouk polynomials, orthogonal arrays

We develop a combinatorial method for computing and reducing of the possibilities of distance distributions of ternary orthogonal array (TOA) of given parameters $(n, M, \tau)$. Using relations between distance distributions of arrays under consideration and their relatives we prove certain constraints on the distance distributions of TOAs. This allows us to collect rules for removing distance distributions as infeasible. The main result is nonexistence of $(17,108,34)$ TOA. Our approach allows substantial reduction of the number of feasible distance distributions for known arrays. This could be helpful for other investigations over the classification of the ternary orthogonal arrays.

2010 MSC

Primary: 05B15; Secondary: 94B25

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