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

  • 제34권7C호
  • /
  • Pages.635-639
  • /
  • 2009
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  • 1226-4717(pISSN)
  • /
  • 2287-3880(eISSN)
한국통신학회 (The Korean Institute of Commucations and Information Sciences)
권호 표지

행백터 집합이 벡터공간을 이루는 하다마드 행렬의 동치관계

Equivalence of Hadamard Matrices Whose Rows Form a Vector Space

  • 진석용 (연세대학교 전기전자공학파 부호및암호 연구실) ;
  • 김정헌 (삼성전자) ;
  • 박기현 (연세대학교 전기전자공학파 부호및암호 연구실) ;
  • 송홍엽 (연세대학교 전기전자공학파 부호및암호 연구실)
  • 발행 : 2009.07.31
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초록

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.

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.

키워드

참고문헌

  1. S. S. Agaian, Hadamard Matrices and Their Applications, Lecture Notes in Mathematics 1168, Springer-Verlag, 1985.
  2. S. W. Golomb and G. Gong, Signal Design for Good Correlation, Cambridge University Press, 2005.
  3. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland,1977, Tenth impression, 1998.
  4. H.-Y. Song and S. W. Golomb, "Some newconstructions for simplex codes," IEEE Transactionson Information Theory, 40:(2), pp.504- 507, March, 1994. https://doi.org/10.1109/18.312174
  5. J. Seberry and M. Yamada, "Hadamard matrices,sequences, and block designs," in ContemporaryDesign Theory, edited by J. H. Dinitz and D.R. Stinson, John Wiley & Sons, pp.431-560,1992.
  6. N. J. A. Sloane and S. Plouffee, The Encyclopedia of Integer Sequences, Academic Press, 1995. See also: N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, http://www. research.att.com/~njas/sequences/A007299.
  7. N. J.A.Sloane, "My favorite integer sequences,"in Sequences and Their Applications, edited by C. Ding, T. Helleseth and H. Niederreiter, Springer, 1999, pp.103-130.See also the extended version: http://www.research.att.com/~njas/doc /sg.pdf
  8. R. Craigen and H. Kharaghani, "Hadamard matrices and Hadamard designs," in Handbook of Combinatorial Designs, 2nd Ed., edited by C. J. Colbourn and J. H. Dinitz, Chapman & Hall/CRC, 2007, pp.273-280.
  9. S. Lang, Linear Algebra, Third Edition, Springer,1987.
  10. S. W. Golomb, Shift Register Sequences, Revised Edition, Aegean Park Press, 1982, originally published by Hoden-Day in 1967.
  11. H.-Y. Song, "Feedback shift register sequences,"in Wiley Encyclopedia of Telecommunications, edited by J. G. Proakis, John Wiley & Sons, pp.789-802, 2003.
  12. R. K. Yarlagadda and J. E. Hershey, Hadamard Matrix Analysis and Synthesis, Kluwer Academic Publishers, 1997.
  13. K. W. Henderson, "Comment on 'Computations of the fast Walsh-Fourier transform," IEEE Transactions on Computers, 19:(9), pp.850-851, September, 1970. https://doi.org/10.1109/T-C.1970.223054
  14. A. Lempel, "Matrix factorization over GF(2)and trace-orthogonal bases of GF(2n),"SIAM Journal of Computation, 4:(2), pp.175-186, June, 1975. https://doi.org/10.1137/0204014