On the k-error linear complexity of sequences with period 2pn over GF(q) |
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Authors: | Jianqin Zhou |
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Affiliation: | (1) Sabancı University, MDBF, Orhanlı, Tuzla, 34956 İstanbul, Turkey |
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Abstract: | In this paper, we first optimize the structure of the Wei–Xiao–Chen algorithm for the linear complexity of sequences over GF(q) with period N = 2p n , where p and q are odd primes, and q is a primitive root modulo p 2. The second, an union cost is proposed, so that an efficient algorithm for computing the k-error linear complexity of a sequence with period 2p n over GF(q) is derived, where p and q are odd primes, and q is a primitive root modulo p 2. The third, we give a validity of the proposed algorithm, and also prove that there exists an error sequence e N , where the Hamming weight of e N is not greater than k, such that the linear complexity of (s + e) N reaches the k-error linear complexity c. We also present a numerical example to illustrate the algorithm. Finally, we present the minimum value k for which the k-error linear complexity is strictly less than the linear complexity. |
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