## Lethbridge Number Theory and Combinatorics Seminar: Sho Suda

• Date: 03/13/2024
• Time: 13:45
Lecturer(s):
Sho Suda, National Defense Academy of Japan
Location:

University of Lethbridge

Topic:

On extremal orthogonal arrays

Description:

An orthogonal array with parameters $$(N,n,q,t)$$ ($$OA(N,n,q,t)$$ for short) is an $$N\times n$$ matrix with entries from the alphabet $$\{1,2,...,q\}$$ such that in any of its $$t$$ columns, all possible row vectors of length $$t$$ occur equally often. Rao showed the following lower bound on $$N$$ for $$OA(N,n,q,2e)$$:
$N\geq \sum_{k=0}^e \binom{n}{k}(q-1)^k,$
and an orthogonal array is said to be complete or tight if it achieves equality in this bound. It is known by Delsarte (1973) that for complete orthogonal arrays $$OA(N,n,q,2e)$$, the number of Hamming distances between distinct two rows is $$e$$. One of the classical problems is to classify complete orthogonal arrays.
We call an orthogonal array $$OA(N,n,q,2e-1)$$ extremal if the number of Hamming distances between distinct two rows is $$e$$. In this talk, we review the classification problem of complete orthogonal arrays with our contribution to the case $$t=4$$ and show how to extend it to extremal orthogonal arrays. Moreover, we give a result for extremal orthogonal arrays which is a counterpart of a result in block designs by Ionin and Shrikhande in 1993.

Other Information:

Time: 1.45pm Mountain/ 12.45pm Pacific

Location: M1060 (Markin Hall)