Project/Area Number  07650436 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
情報通信工学

Research Institution  Kyushu 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)

CoInvestigator(Kenkyūbuntansha) 
UEHARA Satoshi Kyushu Institute of Technology, Dept.Computer Sci.and Electronics, Research Assi, 情報工学部, 助手 (90213389)
MORIUCHI Tsutomu Yatsushiro National College of Technology, Dept.Information and Electronics Engi, 情報電子工学科, 教授 (10124158)

Project Fiscal Year 
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)

Keywords  Pseudorandom Sequences / Randomness / Linear Complexity / Reducing the Instability / kError Linear Complexity / Maximum Order Complexity / 擬似乱数系列 / 乱数系列らしさ / linear complexity / 不安定性の解消 / Kerror linear complexity / maximun order complexity / kerror linear complexity / maximam ordor complexity / kerror 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) onesymbol substitution, (2) onesymbol insertion or (3) onesymbol 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 kerror LC (kLC) 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 kLC and MOC for reducing the insstability of LC and secondly develop an efficient method for computing kLC. Main results are summarized as follows. 1.The original StampMartin algorithm (1993) for computing the kLC of binary periodic sequences with period 2^n can be modified to find an error vector which gives the value of the kLC by adding it to one period of the given sequence. In practical applications of kLC finding an error vector is important. 2.Our new method for computing both of the kLC 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 msequence over GF (q) by any of (1) onesymbol substitution, (2) onesymbol insertion and (3) onesymbol 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 onesymbol substitution.
