1996 Fiscal Year Final Research Report Summary
Methods for Reducing the Instability of Linear Complexity of Sequences
| Project/Area Number |
07650436
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
情報通信工学
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| Research Institution | Kyushu Institute of Technology |
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Principal Investigator |
IMAMURA Kyoki Kyushu Institute of Technology, Dept.Computer Sci.and Electronics, Professor, 情報工学部, 教授 (60037950)
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| 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)
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| Project Period (FY) |
1995 – 1996
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| Keywords | Pseudorandom Sequences / Randomness / Linear Complexity / Reducing the Instability / k-Error Linear Complexity / Maximum Order Complexity |
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| 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.
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