Abstract
Binary sequences with optimal autocorrelation and large linear complexity have important applications in cryptography and communications. Very recently, a class of binary sequences of period 4p with optimal autocorrelation was proposed by interleaving four suitable Ding–Helleseth–Lam sequences (Des. Codes Cryptogr., https://doi.org/10.1007/s10623-017-0398-5), where p is an odd prime with \(p \equiv 1(\bmod 4)\). The objective of this paper is to determine the minimal polynomial and the linear complexity of this class of binary optimal sequences via a sequence polynomial approach. It turns out that this class of sequences has quite good linear complexity.
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Acknowledgements
The author is very grateful to the reviewers and the Editor for their valuable comments that improved the presentation and quality of this paper. This work was supported by the Natural Science Foundation of China under Grants 11571285 and 61661146003, and the Sichuan Provincial Youth Science and Technology Fund under Grant 2016JQ0004.
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Fan, C. The linear complexity of a class of binary sequences with optimal autocorrelation. Des. Codes Cryptogr. 86, 2441–2450 (2018). https://doi.org/10.1007/s10623-018-0456-7
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DOI: https://doi.org/10.1007/s10623-018-0456-7