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Hadamard Matrices Modulo 5 |
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| Authors: | Moon Ho Lee Ferenc Szöll?si |
| Institution: | 1. Division of Electronics and Information Engineering, Chonbuk National University, Jeonju, Republic of Korea;2. Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary |
| Abstract: | In this paper, we introduce modular symmetric designs and use them to study the existence of Hadamard matrices modulo 5. We prove that there exist 5‐modular Hadamard matrices of order n if and only if  or  . In particular, this solves the 5‐modular version of the Hadamard conjecture. |
| Keywords: | Modular Hadamard matrix combinatorial design modular symmetric design 2000 Mathematics Subject Classification: Primary 05B20 secondary 05B05 |