Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pn-periodic Sequences over GF(q)

NIU Zhihua; KONG Deyu

doi:10.11999/JEIT170972

Volume 40 Issue 7

Jul. 2018

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Article Navigation > Journal of Electronics & Information Technology > 2018 > 40(7): 1723-1730

NIU Zhihua, KONG Deyu. Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pn-periodic Sequences over GF(q)[J]. Journal of Electronics & Information Technology, 2018, 40(7): 1723-1730. doi: 10.11999/JEIT170972

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NIU Zhihua, KONG Deyu. Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pⁿ-periodic Sequences over GF(q)[J]. Journal of Electronics & Information Technology, 2018, 40(7): 1723-1730. doi: 10.11999/JEIT170972

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Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pⁿ-periodic Sequences over GF(q)

doi: 10.11999/JEIT170972

NIU Zhihua^①② KONG Deyu^①

Funds:

Shanghai Natural Science Foundation (16ZR1411200, 17ZR1409800), The National Nature Science Foundation of China (61772022, 61572309, 61462077)

Received Date: 2017-10-20
Rev Recd Date: 2018-01-15
Publish Date: 2018-07-19

Abstract

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.
- Cryptography、Periodic sequence、Linear complexity、k-error linear complexity、Error sequence,

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References(21)

References

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