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Correlation measure,linear complexity and maximum order complexity for families of binary sequences
Institution:1. Key Laboratory of Applied Mathematics of Fujian Province University, Putian University, Putian, Fujian 351100, PR China;2. Department of Computer Science, Universidad Rey Juan Carlos, Madrid, Spain;3. Department of Mathematics, Statistics and Computer Science, University of Cantabria, Santander, Spain;4. Scientific Technology, 8 Cecil Street, Brighton East 3187, Melbourne, Australia;1. Applied Algebra and Optimization Research Center, Sungkyunkwan University, Suwon, Republic of Korea;2. Institute of Mathematical Sciences, Ewha Womans University, Seoul, Republic of Korea;1. University of Primorska, UP IAM, Muzejski trg 2, 6000 Koper, Slovenia;2. University of Primorska, UP FAMNIT, Glagolja?ka 8, 6000 Koper, Slovenia;3. IMFM, Jadranska 19, 1000 Ljubljana, Slovenia;1. Universidad Rey Juan Carlos, Madrid, Spain;2. Aarhus University, Aarhus, Denmark;3. Queen''s University Belfast, Belfast, UK;1. Department of Mathematics, University of Auckland, 38 Princes Street, Auckland Central, Auckland 1010, New Zealand;2. School of Mathematics and Statistics, University of Canterbury, Private bag 4800, 8140 Christchurch, New Zealand;1. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA;2. Department of Informatics, University of Bergen, Bergen, Norway;3. Department of Mathematics, University of Trento, Trento, Italy;1. School of Mathematics and Physics, University of South China, Hengyang, Hunan, 421001, China;2. Science and Technology on Communication Security Laboratory, Chengdu 610041, Sichuan, China;3. School of Computer Sciences, Fudan University, Shanghai 200433, China;4. Shanghai Engineering Research Center of Blockchain, Shanghai 200433, China;5. Key Laboratory for Information Science of Electromagnetic Waves (MoE), Shanghai 200433, China;6. Mathematics and Science College of Shanghai Normal University, Shanghai, 200234, China;7. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China
Abstract:The correlation measure of order k is an important measure of pseudorandomness for binary sequences. This measure tries to look for dependence between several shifted versions of a sequence. We study the relation between the correlation measure of order k and two other pseudorandom measures: the Nth linear complexity and the Nth maximum order complexity. We simplify and improve several state-of-the-art lower bounds for these two measures using the Hamming bound as well as weaker bounds derived from it.
Keywords:Pseudorandom sequences  Binary sequences
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