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Methods for Reducing the Instability of Linear Complexity of Sequences

Research Project

Project/Area Number 07650436
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 情報通信工学
Research InstitutionKyushu Institute of Technology

Principal Investigator

IMAMURA Kyoki  Kyushu Institute of Technology, Dept.Computer Sci.and Electronics, Professor, 情報工学部, 教授 (60037950)

Co-Investigator(Kenkyū-buntansha) MORIUCHI Tsutomu  Yatsushiro National College of Technology, Dept.Information and Electronics Engi, 情報電子工学科, 教授 (10124158)
UEHARA Satoshi  Kyushu Institute of Technology, Dept.Computer Sci.and Electronics, Research Assi, 情報工学部, 助手 (90213389)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1996: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1995: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsPseudorandom Sequences / Randomness / Linear Complexity / Reducing the Instability / k-Error Linear Complexity / Maximum Order Complexity / k-error linear complexity / maximam ordor complexity / Linear Complexity / k-error Linear Complexity / 計算法
Research Abstract

Linear complexity (LC) has been used as a convenient measure for evaluating the randomness of pseudorandom sequences in the field of communication engineerring. Recently it was shown by the authors that the LC of a periodic sequence increases to the maximum value (=its period) by such minimum changes as (1) one-symbol substitution, (2) one-symbol insertion or (3) one-symbol deletion per each period. Such an instability of LC is not desirable as a measure of complexity of sequences.
In order to reduce the instability of LC it seems to be effective to use two kinds of generalizations of LC,i.e., (1) the k-error LC (k-LC) which uses the same linear model as LC for generating sequences and (2) the MOC (Maximum Order Complexity) which uses the nonlinear model for generating sequences. In this research project we firstly investigate the effectiveness of k-LC and MOC for reducing the insstability of LC and secondly develop an efficient method for computing k-LC.
Main results are summarized as follows.
1.The original Stamp-Martin algorithm (1993) for computing the k-LC of binary periodic sequences with period 2^n can be modified to find an error vector which gives the value of the k-LC by adding it to one period of the given sequence. In practical applications of k-LC finding an error vector is important.
2.Our new method for computing both of the k-LC and an error vector of binary periodic sequence with period 2^n can be generalized to the case of periodic sequences over GF (q) with period q^n in a very natural way.
3.New tight upper and lower bounds can be found about the MOC of the sequence obtained from an m-sequence over GF (q) by any of (1) one-symbol substitution, (2) one-symbol insertion and (3) one-symbol deletion per each period.
4.Similar instability of LC can be shown to happen for periodic sequences over a finite rings, Z_4 and Z_8 by one-symbol substitution.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] 上原 聡: "Linear complexity of periodic sequences obtained from GF(q) sequences with period q^n-1 by one-symbol insertion" IEICE Trans.Fundamentals.E79-A. 1739-1740 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 上原 聡: "Characteristic polynomials of binary complementary sequences" IEICE Trans.Fundamentals. E80-A. 193-196 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 上原 聡: "Linear complexity of periodic Sequence obtained from a sequence over GF(p) with period p^n-1 by one-symbol deletion" IEICE Trans.Fundamentals. E80-A(採録決定). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 上原 聡: "Value distribution of linear complexity for pary periodic sequences with period p^n,p a prime" IEICE Trans.Fundamentals. E80-A(採録決定). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Zonduo Dai: "Linear complexity for one-symbol substitution of a periodic sequence over GF(q)" IEICE Trans.Fundamentals. (採録決定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 戒田 高康: "J.Jatlar,R.H.C.Yap(eds.)-Lecture Notes in Computer Science 1179" Springer-Verlag, 10 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S.Uehara and K.Imamura: ""Linear complexity of periodic sequences obtained from GF (q) sequences with period q^n-1 by one-symbol insertion"" IEICE Trans.Fundamentals. vol.E79-A. 1739-1740 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Kaida, S.Uehara and K.Imamura: ""Computation of the k-error linear complexity of binary sequences with period 2^n"" J.Jaffar and H.C.Yap (eds.), Concurrency and Parallelism, Programming, Networking, and Security (Springer LNCS 1179). 182-191 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S.Uehara and K.Imamura: ""Characteristic polynomials of binary complementary sequences"" IEICE Trans.Fundamentals. vol.E80-A. 193-196 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S,Uehara and K.Imamura: ""Linear complexity of periodic sequences obtained from a sequence over GF (p) with period p^n-1 by one-symbol deletion"" IEICE Trans.Fundamentals. vol.E80-A (to be published). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S.Uehara and K.Imamura: ""Value distribution of linear complexity for p-ary periodic sequences with period p^n, p a prime"" IEICE Trans.Fundamentals. vol.E80-A (to be published). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Z.Dai and K.Imamura: ""Linear complexity for one-symbol substitution of a periodic sequence over GF (q)"" IEEE Trans.on Information Theory.acceoted for publication.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 上原 聡: "Linear complexity of periodic sequences obtained from GF(a) sequences with period q^n-1 by one-symbol in sertion" IEICE Trans.Fundamentals.E79-A. 1739-1746 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 上原 聡: "Characteristic polynomials of binary complementary sequences" IEICE Trans.Fundamentals. E80-A. 193-196 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 上原 聡: "Linear complexity of periodic sequences obtained from a sequence over GF(p) with period p^n-1 by one-symbol deletion" IEICE Trans.Fundamentals. E80-A(採録決定). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 上原 聡: "Value distribution of linear complexity for pary periodic sequences with period p^n,p a prime" IEICE Trans.Fundamentals. E80-A(採録決定). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Zongduo Dai: "Linear complexity for one-symbol substitution of a periodic suquence over GF(q)" IEEE Trans.on Information Theory. (採録決定).

    • Related Report
      1996 Annual Research Report
  • [Publications] 戒田 高康: "Computation of the k-error linear complexity of binary sequences with period 2^n" Lacture Notes in Computer Science. 1179. 182-191 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 松藤信哉: "On p-ary bent sequences" IEICE Trans.Fundamentals. E78-A. 1257-1266 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 上原聡: "相補系列の生成多項式" Proc.18th Symp.on Information Theory and Its Applications. 281-284 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 上原聡: "大きなLinear Complexityを持つ周期系列の構成法" Proc.18th Symp.on Information Theory and Its Applications. 285-288 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 上原聡: "相補系列の周期系列としてのLC Profileと相関特性" 電子情報通信学会情報理論研究会技術報告. 95. 45-49 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 今村恭己: "大矢雅則他編「数理情報科学事典」("ガロア体"について分担執筆)" 朝倉書店, 2 (1995)

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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