The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Equivalence of Hadamard Matrices Whose Rows Form a Vector Space

행백터 집합이 벡터공간을 이루는 하다마드 행렬의 동치관계

  • 진석용 (연세대학교 전기전자공학파 부호및암호 연구실) ;
  • 김정헌 (삼성전자) ;
  • 박기현 (연세대학교 전기전자공학파 부호및암호 연구실) ;
  • 송홍엽 (연세대학교 전기전자공학파 부호및암호 연구실)
  • Published : 2009.07.31
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Abstract

In this paper, we show that any two Hadamard matrices of the same size are equivalent if they have the property that the rows of each Hadamard matrix are closed under binary vector addition. One of direct consequences of this result is that the equivalence between cyclic Hadamard matrices constructed by maximal length sequences and Walsh-Hadamard matrix of the same size generated by Kronecker product can be established.

본 논문에서는 행벡터의 집합이 이진 벡터합 연산에 관해 닫혀있는 모든 하다마드 (Hadmard) 행렬들은 서로 동치(equivalent) 임융 증명한다. 이를 이용하면, 최대길이 수열로부터 생성된 순회 (cyclic) 하다마드 행렬과 크로네커 (Kronecker) 곱에 의해 생성된 월쉬-하다마드 (Walsh-Hadamard) 행렬이 동치임을 간단히 보일 수 있다.

Keywords

References

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