Universal p-ary designs

2020/12/08 by Liam Jolliffe, Jolliffe, Liam
Engineering · Mathematics · #graph theory and CDMA systems #Limits and Structures in Graph Theory #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2012.04202

Abstract

We investigate p-ary t-designs which are simultaneously designs for all t, which we call universal p-ary designs. Null universal designs are well understood due to Gordon James via the representation theory of the symmetric group. We study non-null designs and determine necessary and sufficient conditions on the coefficients for such a design to exist. This allows us to classify all universal designs, up to similarity.

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