Journal of the Institute of Electronics Engineers of Korea TC (대한전자공학회논문지TC)

The Institute of Electronics and Information Engineers (대한전자공학회)
권호 표지

Construction of Jacket Matrices Based on q-ary M-sequences

q-ary M-sequences에 근거한 재킷 행렬 설계

  • 발라카난 (전북대학교 전자정보공학부) ;
  • 김정기 (전북대학교 전자정보공학부) ;
  • ;
  • 이문호 (전북대학교 전자정보공학부)
  • Published : 2008.07.25
Download PDF
⟨ Previous Next ⟩

Abstract

As with the binary pseudo-random sequences q-ary m-sequences possess very good properties which make them useful in many applications. So we construct a class of Jacket matrices by applying additive characters of the finite field $F_q$ to entries of all shifts of q-ary m-sequence. In this paper, we generalize a method of obtaining conventional Hadamard matrices from binary PN-sequences. By this way we propose Jacket matrix construction based on q-ary M-sequences.

이진 pseudo-random 시퀀스를 갖는 q-ary M-sequence는 많은 적용 분야에 사용할 수 있는 유리한 특성을 가지고 있다. 본 논문은 유한장 $F_q$의 덧셈 특성을 이용하여 q-ary M-sequence 원소의 시프트로 재킷 행렬의 새로운 계열을 설계하고 있다. 또한, 이진 PN-시퀀스로부터 기존의 하다마드 행렬을 얻는 방법을 일반화하였고, 제안한 방법으로 q-ary M-sequence에 근거한 재킷행렬을 보인다.

Keywords

References

  1. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, Elsevier Science Publishers B.V., 1977
  2. R. Lidl and H. Niderreiter, Introduction to Finite Fields and their Applications, Cambridge University Press, 1994
  3. M.H. Lee, "A New Reverse Jacket Transform and its Fast Algorithm", IEEE Transactions Circuits Syst.-II, vol.47, no 1, pp. 39-47, January 2000 https://doi.org/10.1109/82.818893
  4. M.H. Lee, B.S. Rajan, and J.Y. Park, "A Generalized Reverse Jacket Transform", IEEE Transactions Circuits Syst.-II, vol. 48, no 7, pp. 684-691, July 2001 https://doi.org/10.1109/82.958338
  5. M.H. Lee and J.Hou, "Fast Block Inverse Jacket Transform", IEEE Signal Processing Letters, vol. 13, no 8, pp.461-464, August 2006 https://doi.org/10.1109/LSP.2006.873660
  6. J. Hou and M.H. Lee, "Complex Values OVSF and Jacket Matrices", IEICE Trans. Fundamentals, vol.E98-A, no.11, pp. 3363-3367, Nov.2006
  7. J. Hou, M.H. Lee, and J.Y. Park, "New Polynomial Construction of Jacket Transform", IEICE Transactions Fundamentals, vol. E86-A, no 3, pp. 652-660, March 2003