BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sho Suda (National Defense Academy of Japan) DTSTART:20240313T194500Z DTEND:20240313T204500Z DTSTAMP:20260423T052447Z UID:NTC/38 DESCRIPTION:Title: On extremal orthogonal arrays\nby Sho Suda (National Defense Academy of J apan) as part of Lethbridge number theory and combinatorics seminar\n\nLec ture held in University of Lethbridge: M1060 (Markin Hall).\n\nAbstract\nA n orthogonal array with parameters $(N\,n\,q\,t)$ ($OA(N\,n\,q\,t)$ for sh ort) is an $N\\times n$ matrix with entries from the alphabet $\\{1\,2\,.. .\,q\\}$ such that in any its $t$ columns\, all possible row vectors of le ngth $t$ occur equally often. \nRao showed the following lower bound on $N $ for $OA(N\,n\,q\,2e)$: \n\\[\nN\\geq \\sum_{k=0}^e \\binom{n}{k}(q-1)^k\ , \n\\]\nand an orthogonal array is said to be complete or tight if it ach ieves equality in this bound. \nIt is known by Delsarte (1973) that for co mplete orthogonal arrays $OA(N\,n\,q\,2e)$\, the number of Hamming distanc es between distinct two rows is $e$. \nOne of the classical problems is to classify complete orthogonal arrays. \n\nWe call an orthogonal array $OA (N\,n\,q\,2e-1)$ extremal if the number of Hamming distances between disti nct two rows is $e$. \nIn this talk\, we review the classification proble m of complete orthogonal arrays with our contribution to the case $t=4$ an d show how to extend it to extremal orthogonal arrays. \nMoreover\, we giv e a result for extremal orthogonal arrays which is a counterpart of a resu lt in block designs by Ionin and Shrikhande in 1993.\n LOCATION:https://researchseminars.org/talk/NTC/38/ END:VEVENT END:VCALENDAR