A method to construct generalized balanced tournament designs
Songchol Kim, Changil Rim
TL;DR
This paper introduces a new construction method for generalized balanced tournament designs (GBTDs) and proves the existence of GBTD(p,p) for all primes p ≥ 3, advancing combinatorial design theory.
Contribution
The paper presents a novel construction technique for GBTDs and establishes their existence for all prime numbers p ≥ 3.
Findings
Existence of GBTD(p,p) for all primes p ≥ 3
New construction method for GBTDs
Enhanced understanding of combinatorial design structures
Abstract
A generalized balanced tournament design, or a GBTD(k, m) in short, is a (km, k, k-1)-BIBD defined on a km-set V . Its blocks can be arranged into an m\times(km-1) array in such a way that (1) every element of V is contained in exactly one cell of each column, and (2) every element of V is contained in at most k cells of each row. In this paper, we present a new construction for GBTDs and show that a GBTD(p,p) exists for any prime number p \geq 3.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography