q-Analogs of t-Wise Balanced Designs from Borel Subgroups

2013/08/08 by Michael Braun, Braun, Michael
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cooperative Communication and Network Coding

paper · pdf · doi:10.48550/arxiv.1308.1829

Abstract

A t-(n,K,λ;q) design, also called the q-analog of a t-wise balanced design, is a set \mathcal B of subspaces with dimensions contained in K of the n-dimensional vector space \mathbb F_qⁿ over the finite field with q elements such that each t-subspace of \mathbb F_qⁿ is contained in exactly λ elements of \mathcal B. In this paper we give a construction of an infinite series of nontrivial t-(n,K,λ;q) designs with |K|=2 for all dimensions t≥ 1 and all prime powers q admitting the standard Borel subgroup as group of automorphisms. Furthermore, replacing q=1 gives an ordinary t-wise balanced design defined on sets.

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