• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.5
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• pp.9-17
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• 2013

In this paper we introduce modular symmetric designs and use them to study the existence of Hadamard-Jacket matrices modulo 3/5. We prove that there exist 5-modular Hadamard-Jacket matrices of order n if and only if n≢3.7 (mod 10) and n≢6,11. In particular, this solves the 5-modular version of the Hadamard conjecture.