Date of Award
2019
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Magliveras, Spyros S.
Abstract
It was not until the 20th century that combinatorial design theory was studied as a formal subject. This field has many applications, for example in statistical experimental design, coding theory, authentication codes, and cryptography. Major approaches to the problem of discovering new t-designs rely on (i) the construction of large sets of t designs, (ii) using prescribed automorphism groups, (iii) recursive construction methods. In 2017 and 2018, Tran Van Trung introduced new recursive techniques to construct t – (v, k, λ) designs. These methods are of purely combinatorial nature and require using "ingredient" t-designs or resolutions whose parameters satisfy a system of non-linear equations. Even after restricting the range of parameters in this new method, the task is computationally intractable. In this work, we enhance Tran Van Trung's "Basic Construction" by a robust and efficient hybrid computational apparatus which enables us to construct hundreds of thousands of new t – (v, k, Λ) designs from previously known ingredient designs. Towards the end of the dissertation we also create a new family of 2-resolutions, which will be infinite if there are infinitely many Sophie Germain primes.
Extent
180 p.
Recommended Citation
Lopez, Oscar A., "An Algorithmic Approach to Tran Van Trung's Basic Recursive Construction of t-Designs" (2019). Electronic Theses and Dissertations 2010 - 2019. 2090.
https://digitalcommons.fau.edu/etd_general_6/2090
Identifier
FA00013233
Comments
Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2019.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.