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Article Navigation >  Journal of University of Electronic Science and Technology of China  > 2011  >  40(3): 379-382

CHEN Jun, CHEN Yun, WU Zhen. Research on the Linear Complexity for a Family of Large Size of p-ary Sequences with Low Correlation[J]. Journal of University of Electronic Science and Technology of China, 2011, 40(3): 379-382. doi: 10.3969/j.issn.1001-0548.2011.03.010
Citation: CHEN Jun, CHEN Yun, WU Zhen. Research on the Linear Complexity for a Family of Large Size of p-ary Sequences with Low Correlation[J]. Journal of University of Electronic Science and Technology of China, 2011, 40(3): 379-382. doi: 10.3969/j.issn.1001-0548.2011.03.010
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Research on the Linear Complexity for a Family of Large Size of p-ary Sequences with Low Correlation

doi: 10.3969/j.issn.1001-0548.2011.03.010
  • 1.

    School of Information Science and Technology,South Jiaotong University Chengdu 610031;

  • 2.

    Information Security Institute,Chengdu University of Information Technology Chengdu 610225

  • Received Date: 2010-02-05
  • Rev Recd Date: 2010-11-25
  • Publish Date: 2011-06-15
  • Constructing a large family of p-ary sequences with large linear complexity and low correlation is very important for code division multiple access (CDMA) communication systems. By use of Klapper's method and d-form function, a large family S(r) of p-ary sequences with low correlation is constructed. Such family contains p2n sequences of period pn-1 with maximal nontrivial correlation value 4p(n)/(2)-1. The minimal and maximal linear complexity of the sequences family are proven to be 2(n)/(2)-2n and 3(n)/(2)-1×2(n)/(2)-2n for p > 5 and r=(pm-1-1)/(p-1), respectively. It is also proven that the maximal and minimal linearcomplexity of the sequences set are larger than 3(n)/(4)-1×2(n)/(4)-2n and 2(n)/(4)-2n for p=3, 5 and r=(pm-1-1)/(p-1), respectively. This sequences family can greatly improve the security of CDMA communication systems.
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Research on the Linear Complexity for a Family of Large Size of p-ary Sequences with Low Correlation

doi: 10.3969/j.issn.1001-0548.2011.03.010
  • 1. School of Information Science and Technology,South Jiaotong University Chengdu 610031;
  • 2. Information Security Institute,Chengdu University of Information Technology Chengdu 610225
  • Received Date: 2010-02-05
  • Rev Recd Date: 2010-11-25
  • Publish Date: 2011-06-15

Abstract: Constructing a large family of p-ary sequences with large linear complexity and low correlation is very important for code division multiple access (CDMA) communication systems. By use of Klapper's method and d-form function, a large family S(r) of p-ary sequences with low correlation is constructed. Such family contains p2n sequences of period pn-1 with maximal nontrivial correlation value 4p(n)/(2)-1. The minimal and maximal linear complexity of the sequences family are proven to be 2(n)/(2)-2n and 3(n)/(2)-1×2(n)/(2)-2n for p > 5 and r=(pm-1-1)/(p-1), respectively. It is also proven that the maximal and minimal linearcomplexity of the sequences set are larger than 3(n)/(4)-1×2(n)/(4)-2n and 2(n)/(4)-2n for p=3, 5 and r=(pm-1-1)/(p-1), respectively. This sequences family can greatly improve the security of CDMA communication systems.

CHEN Jun, CHEN Yun, WU Zhen. Research on the Linear Complexity for a Family of Large Size of p-ary Sequences with Low Correlation[J]. Journal of University of Electronic Science and Technology of China, 2011, 40(3): 379-382. doi: 10.3969/j.issn.1001-0548.2011.03.010
Citation: CHEN Jun, CHEN Yun, WU Zhen. Research on the Linear Complexity for a Family of Large Size of p-ary Sequences with Low Correlation[J]. Journal of University of Electronic Science and Technology of China, 2011, 40(3): 379-382. doi: 10.3969/j.issn.1001-0548.2011.03.010
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