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

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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New Family of p-ary Sequences with Optimal Correlation Property and Large Linear Span

최적의 상관 특성과 큰 선형 복잡도를 갖는 새로운 p-진 수열군

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

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.

Keywords

References

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