Abstract.
In earlier papers the authors studied finite pseudorandom binary sequences, and they constructed sequences with strong pseudorandom properties. In these earlier constructions multiplicative characters were used. In this paper a new construction is presented which utilizes properties of additive characters. These new sequences can be computed fast, they are well-distributed relative to arithmetic progressions and their correlations of “small” order are “small”, but the price paid for the fast computation is that the correlations of “large” order can be “large”.
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Mauduit, C., Rivat, J. & Sárközy, A. Construction of Pseudorandom Binary Sequences Using Additive Characters. Monatsh. Math. 141, 197–208 (2004). https://doi.org/10.1007/s00605-003-0112-8
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DOI: https://doi.org/10.1007/s00605-003-0112-8
- 2000 Mathematics Subject Classification: 11K45; 11K06, 11K38, 11L07
- Key words: Pseudo-random, binary sequence, additive character, correlation