Journal of the Institute of Electronics and Information Engineers (전자공학회논문지)

The Institute of Electronics and Information Engineers (대한전자공학회)
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3/5-Modular Hadamard-Jacket Symmetric Matrices

3/5-Modular Hadamard-Jacket 대칭 행렬

  • Park, Ju Yong (Department of Internet, Information & Communication, Shyngyeong University) ;
  • Kim, Jeong Su (Department of Computer, Information & Communication, Korea Soongsil Cyber University) ;
  • Szollosi, Ference (Budapest University of Technology and Economic) ;
  • Lee, Moon Ho (Division of Electronic Engineering, Chonbuk National University)
  • Received : 2012.12.24
  • Published : 2013.05.25
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Abstract

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.

본 논문에서는 modular 대칭 설계에 대해 소개하고 이를 이용하여 Hadamard-Jacket 행렬의 modular 3/5가 존재한다는 것을 제시한다. 그리고 n차 5-modular Hadamard 행렬의 필요충분조건이 n≢3.7 (mod 10)와 n≢6,11 임을 증명한다. 특히 Hadamard-Jacket 추측(conjecture)에 대한 5-modular 버전을 구한다.

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