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RAP opportunity at Air Force Science and Technology Fellowship Program     AF STFP

Finding Efficient Factorial Designs for Test and Evaluation


Air Force Institute of Technology

opportunity location
13.50.00.C0885 AFIT, Wright-Patterson AFB, OH 454337542


name email phone
Dursun Bulutoglu 937.426.0546


Hadamard matrices are used as experimental plans in factor screening in test and evaluation. Finding a Hadamard matrix in general is a difficult open problem. A Legendre pair of length n can be used to construct a Hadamard matrix of order 2n+2 for each odd integer n. Understanding the existence patterns of Legendre pairs will lead to better algorithms for finding Hadamard matrices. This reseach opportunity focuses on applying cyclotomic field extensions for developing a theory to better understand the existence patterns of Legendre pairs. This theory will be used for devoloping improved algorithms for finding Legendre pairs.  

I.S. Kotsireas, C. Koutschan, D.A. Bulutoglu, D.M. Arquette, J.S. Turner, K.J. Ryan: Legendre paits of length 0 mod 5: Special matrices 11: 2023

J.S. Turner, I.S. Kotsireas, DA Bulutoglu, A.J. Geyer: A Legendre pair of length 77 using complementary binary matriceswith fixed marginals:  Designs, Codes , and Cryptography 89:2021

K.T. Arasu, D.A. Bulutoglu, J. Hollon; Legendre G-array pairs and the theorethical unification of several G-array families: Journal of Combinatorial Designs 28:2020

key words
Hadamard matrices; Legendre pairs; Algebraic number theory; Algebraic combinatorics; Cyclotomic field extensions


Citizenship:  Open to U.S. citizens
Level:  Open to Postdoctoral and Senior applicants


Base Stipend Travel Allotment Supplementation
$95,000.00 $5,000.00

Experience Supplement:
Postdoctoral and Senior Associates will receive an appropriately higher stipend based on the number of years of experience past their PhD.

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