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Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pn-periodic Sequences over GF(q) |
NIU Zhihua①② KONG Deyu① |
①(School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China)
②(Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai 200444, China) |
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Abstract The k-error linear complexity of a sequence is a fundamental concept for assessing the stability of the linear complexity. After computing the k-error linear complexity of a sequence, those bits that make the linear complexity reduced also need to be computed. For 2pn-periodic sequence over GF(q) , where p and q are odd primes and q is a primitive root modulo p2, an algorithm is presented, which not only computes the k-error linear complexity of a sequence s but also gets the corresponding error sequence e. A function is designed to trace the vector cost called “trace function”, so the error sequence e can be computed by calling the “trace function”, and the linear complexity of (s+e) reaches the k-error linear complexity of the sequence s.
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Received: 20 October 2017
Published: 08 April 2018
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Fund:Shanghai Natural Science Foundation (16ZR1411200, 17ZR1409800), The National Nature Science Foundation of China (61772022, 61572309, 61462077) |
Corresponding Authors:
NIU Zhihua
E-mail: zhniu@staff.shu.edu.cn
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