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| On the Expected Value of the Linear Complexity and the k-Error Linear Complexity of Periodic Sequences |
| Niu Zhi-hua; Bai En-jian; Xiao Guo-zhen |
| National Key Lab of Integrated Service Networks Xidian Univ., Xi’an 710071 China |
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Abstract Cryptographically strong sequences not only should have a large linear com-plexity, but also no a significant decrease of the linear complexity when a few terms are changed. This requirement leads to the concept of the /c-error linear complexity of periodic sequences. In the following two cases: (1) gcd(N,p) = 1; (2) N= pv, where p denotes the characteristic of the finite field GF(q), the counting function NN,o(c), i.e., the number of N-periodic sequences with given linear complexity c, is showed, the expected value of the linear complexity En,o is determined, and a useful lower bound on the expected value of the k-errov linear complexity EN,κ is established.
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Received: 15 May 2003
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2004, Vol. 26 
