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

  • 제28권9C호
  • /
  • Pages.835-842
  • /
  • 2003
  • /
  • 1226-4717(pISSN)
  • /
  • 2287-3880(eISSN)
한국통신학회 (The Korean Institute of Commucations and Information Sciences)
권호 표지

최적의 상관 특성과 큰 선형 복잡도를 갖는 새로운 p-진 수열군

New Family of p-ary Sequences with Optimal Correlation Property and Large Linear Span

  • 장지용 (서울대학교 전기컴퓨터공학부 부호 및 암호 연구실) ;
  • 김영식 (서울대학교 전기컴퓨터공학부 부호 및 암호 연구실) ;
  • 노종선 (서울대학교 전기컴퓨터공학부 부호 및 암호 연구실) ;
  • ;
  • ;
  • ;
  • Tor Helleseth (Department of Informatics, University of Bergen)
  • 발행 : 2003.09.01
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초록

For an odd prime p and integer n, m and k such that n=(2m＋1)ㆍk, a new family of p-ary sequences of period p$^{n}$ -1 with optimal correlation property is constructed using the p-ary Helleseth-Gong sequences with ideal autocorrelation, where the size of the sequence family is p$^{n}$ . That is, the maximum nontrivial correlation value R$_{max}$ of all pairs of distinct sequences in the family does not exceed p$^{n}$ 2/ ＋1, which means the optimal correlation property in terms of Welch's lower bound. It is also derived that the linear span of the sequences in the family is (m＋2)ㆍn except for the m-sequence in the family.

키워드

참고문헌

  1. Linear Groups with on Exposition of the Galois Field Theory, L.E.Dickson
  2. IEEE Trans. Inform. Theory New nonbinary sequences with ideal towlevel autocorrelation function T.Helleseth;G.Gong
  3. IEEE Trans. Inform. Theory v.37 Primephase sequences with periodic correlation prooperties better than binary sequences P.V.Kumar;O.Moreno
  4. Journal of Combinatorial Theory, Series A. v.40 Generalized bent functions and their properties P.V.Kumar;R.A.Scholtz;L.R.Welch
  5. IEEE Trans. Inform. Theory v.38 Maximal families of bent sequences A.Lempel;M.Cohn
  6. Encyclopedia of Mathematics and its Applications v.20 Finite Fields R.Lidl;H.Niederreiter
  7. IEEE Trans. Inform. Theory v.38 Nonbinary Kasami sequences over GF(p) S.C.Liu;J.F.Komo
  8. The Theory of Error-Correctiong Codes F.J.McWillianms;N.J.A.Sloane
  9. IEEE Trans. Inform. Theory v.41 Balanced nonbinary sequences with good periodic correlation properitew obtained from modified Kumar-Moreno sequences T.Moriuchi;K.Imamura
  10. IEEE Trans. Inform. Theory v.28 Bent-function sequences J.D.Olsen;R.A.Scholtz;L.R.Welch
  11. Journal of Combinatorial Theory, Series A. v.20 On bent functions O.S.Rothaus
  12. SLAM J. Comput v.9 no.4 Factorization of symmetric matrices and trace-orthogonal bases in finite fields G.Seroussi;A.Lempel
  13. Spread Spectrum Communications v.1 M.K.Simon;J.K.Omura,R.A.Scholtz;B.K.Levitt
  14. IEEE Trans. Inform. Theory v.20 Lower bounds on the maximal cross correlation of signals L.R.Welch