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

The Institute of Electronics and Information Engineers (대한전자공학회)
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The Toeplitz Circulant Jacket Matrices

The Toeplitz Circulant Jacket 행렬

  • Park, Ju Yong (Department of Internet, Information & Communication, Shyngyeong University) ;
  • Kim, Jeong Su (Department of Computer, Information & Communication, Korea Soongsil Cyber University) ;
  • Szollosi, Ferenc (Budapest University of Technology and Economic) ;
  • Lee, Moon Ho (Division of Electronic Engineering, Chonbuk National University)
  • Received : 2013.02.25
  • Published : 2013.07.25
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Abstract

In this paper we prove that all Jacket matrices are circulant and up to equivalence. This result leads to new constructions of Toeplitz Jacket(TJ) matrices. We present the construction schemes of Toeplitz Jacket matrices and the examples of $4{\times}4$ and $8{\times}8$ Toeplitz Jacket matrices. As a corollary we show that a Toeplitz real Hadamard matrix is either circulant or negacyclic.

본 논문에서는 모든 Toeplitz Jacket 행렬이 순환(circulant)하고 동치(equivalence)에 이름을 보여준다. 순환하고 동치에 이르면 Toeplitz Jacket 행렬의 새로운 구조를 만들 수 있다. Toeplitz Jacket(TJ) 행렬의 구성법을 제시하고 $4{\times}4$과 $8{\times}8$의 Toeplitz Jacket 행렬의 예를 제시 하였다. 따라서 Toeplitz real Jacket 행렬은 순환하거나 negacycle임을 보여준다.

Keywords

Acknowledgement

Supported by : 한국연구재단

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