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On the k-error linear complexity of sequences with period 2p n over GF(q)

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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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Authors and Affiliations

  1. Telecommunication School, Hangzhou Dianzi University, Hangzhou, 310018, China

    Jianqin Zhou

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  1. Jianqin Zhou
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Correspondence to Jianqin Zhou.

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Communicated by P. Wild.

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Zhou, J. On the k-error linear complexity of sequences with period 2p n over GF(q). Des. Codes Cryptogr. 58, 279–296 (2011). https://doi.org/10.1007/s10623-010-9379-7

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  • DOI: https://doi.org/10.1007/s10623-010-9379-7

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