Research On The K-error Linear Complexity Distribution Of Periodic Sequence

The linear complexity and the k-error linear complexity have been used as importantsecurity measures for key stream sequence strength.The high security strength key streamshould has high linear complexity and k-error linear complexity.Linear complexity and k-errorlinear complexity have been important research question in key steam,in this paper,by studyingthe linear complexity of periodic sequence, discussed on the k-error linear complexitydistribution of periodic sequence. First,by using the sieve method of combinatorics,investigatethe8-error linear complexity distribution of2ⁿperiodic binary sequences with linearcomplexity less than2ⁿ;Second,by using the sieve method of combinatorics again, investigatethe1-error linear complexity distribution ofpⁿperiodic p-ary sequences with linearcomplexity equalpⁿ;Lastly,by studying the Xiao-Wei-Lam-Imamura Algorithm,discuss thesome k-error linear complexity distribution ofpⁿperiodic binary sequences. The followingmain results are obtained:1. We call the2ⁿ-periodic binary sequences with linear complexity less than2ⁿare2ⁿ-periodic balance binary sequences.Based on Games-Chan algorithm and using thesieve method,8-error linear complexity distribution of2ⁿ-periodic balanced binarysequences is discussed,and the complete counting functions on2ⁿ-periodic balancedbinary sequences with8-error linear complexity2^n-2，2^n-3，2^n-4n and2^n-32^n-j jarederived respectively.2. Based on generalized Games-Chan algorithm and using the sieve method,1-errorlinear complexity distribution ofpⁿ-periodic p-ary sequences with linear complixityequalpⁿis discussed, the number of sequences with certain1-error linearcomplexity is given.3. The k-error linear complexity distribution ofpⁿ-periodic binary sequences isdiscussed. Based on the XWLI algorithm,1-error linear complexity distribution ofpⁿ-periodic binary sequences with linear complixity less thanpn1is discussed, andthe complete counting functions onpⁿ-periodic binary sequences with1-error linearcomplexity less thanpn1are derived. 4. Based on the XWLI algorithm,2-error linear complexity distribution of3n-periodicbinary sequences with linear complixity less than3n2is discussed, and the completecounting functions on3n-periodic binary sequences with2-error linear complexityless than3n2are derived.