More constructions of pseudorandom lattices of \(k\) symbols
详细信息 查看全文
- 作者：Kit-Ho Mak
- 关键词：Pseudorandom lattices ; Lehmer problem ; Multiplicative characters ; Additive characters ; Pseudorandom measures ; Primary 11K45 ; Secondary 11A07
- 刊名：Monatshefte f篓鹿r Mathematik
- 出版年：2015
- 出版时间：June 2015
- 年：2015
- 卷：177
- 期：2
- 页码：307-323
- 全文大小：470 KB
- 参考文献：1.Ahlswede, R., Mauduit, C., S谩rk枚zy, A.: Large families of pseudorandom sequences of \(k\) symbols and their complexity. I, General Theory of Information Transfer and Combinatorics, Lecture Notes in Comput. Sci., vol. 4123, pp. 293鈥?07. Springer, Berlin (2006)
2.Ahlswede, R., Mauduit, C., S谩rk枚zy, A.: Large families of pseudorandom sequences of \(k\) symbols and their complexity. II, General Theory of Information Transfer and Combinatorics, Lecture Notes in Comput. Sci., vol. 4123, pp. 308鈥?25, Springer, Berlin (2006)
3.B茅rczi, G.: On finite pseudorandom sequences of \(k\) symbols. Period. Math. Hungar. 47(1鈥?), 29鈥?4 (2003)MATH MathSciNet
4.Eichenauer-Herrmann, J., Niederreiter, H.: Bounds for exponential sums and their applications to pseudorandom numbers. Acta Arith. 67(3), 269鈥?81 (1994)MATH MathSciNet
5.Gomez, D., Winterhof, A.: Multiplicative character sums of Fermat quotients and pseudorandom sequences. Period. Math. Hungar. 64(2), 161鈥?68 (2012)View Article MATH MathSciNet
6.Hubert, P., Mauduit, C., S谩rk枚zy, A.: On pseudorandom binary lattices. Acta Arith. 125(1), 51鈥?2 (2006)View Article MATH MathSciNet
7.Liu, H.: A family of pseudorandom binary sequences constructed by the multiplicative inverse. Acta Arith. 130(2), 167鈥?80 (2007)View Article MATH MathSciNet
8.Liu, H., Yang, C.: On a problem of D. H. Lehmer and pseudorandom binary sequences. Bull. Braz. Math. Soc. (N.S.) 39(3), 387鈥?99 (2008)View Article MATH MathSciNet
9.Liu, H.: A large family of pseudorandom binary lattices. Proc. Am. Math. Soc. 137(3), 793鈥?03 (2009)View Article MATH
10.Liu, H.: Large families of pseudorandom binary sequences and lattices by using the multiplicative inverse. Acta Arith. 159(2), 123鈥?31 (2013)View Article MATH MathSciNet
11.Mak, K.-H.: More constructions of pseudorandom sequences of \(k\) symbols. Finite Fields Appl. 25, 222鈥?33 (2014)View Article MATH MathSciNet
12.Mauduit, C., Rivat, J., S谩rk枚zy, A.: Construction of pseudorandom binary sequences using additive characters. Monatsh. Math. 141(3), 197鈥?08 (2004)View Article MATH MathSciNet
13.Mauduit, C., S谩rk枚zy, A.: On finite pseudorandom binary sequences. I. Measure of pseudorandomness, the Legendre symbol. Acta Arith. 82(4), 365鈥?77 (1997)MATH MathSciNet
14.Mauduit, C., S谩rk枚zy, A.: On finite pseudorandom sequences of \(k\) symbols. Indag. Math. (N.S.) 13, 89鈥?01 (2002)View Article MATH MathSciNet
15.Mauduit, C., S谩rk枚zy, A.: Construction of pseudorandom binary sequences by using the multiplicative inverse. Acta Math. Hungar. 108(3), 239鈥?52 (2005)View Article MATH MathSciNet
16.Mauduit, C., S谩rk枚zy, A.: On large families of pseudorandom binary lattices. Unif. Distrib. Theory 2(1), 23鈥?7 (2007)MATH MathSciNet
17.Mauduit, C., S谩rk枚zy, A.: Construction of pseudorandom binary lattices by using the multiplicative inverse. Monatsh. Math. 153(3), 217鈥?31 (2008)View Article MATH MathSciNet
18.M茅rai, L.: Construction of pseudorandom binary lattices based on multiplicative characters. Period. Math. Hungar. 59(1), 43鈥?1 (2009)View Article MATH MathSciNet
19.M茅rai, L.: A construction of pseudorandom binary sequences using rational functions. Unif. Distrib. Theory 4(1), 35鈥?9 (2009)MATH MathSciNet
20.M茅rai, L.: On finite pseudorandom lattices of \(k\) symbols. Monatsh. Math. 161(2), 173鈥?91 (2010)View Article MATH MathSciNet
21.M茅rai, L.: Construction of pseudorandom binary lattices using elliptic curves. Proc. Am. Math. Soc. 139(2), 407鈥?20 (2011)View Article MATH
22.M茅rai, L.: Construction of pseudorandom binary sequences over elliptic curves using multiplicative characters. Publ. Math. Debrecen 80(1鈥?), 199鈥?13 (2012)MATH MathSciNet
23.S谩rk枚zy, A.: On finite pseudorandom binary sequences and their applications in cryptography. Tatra Mt. Math. Publ. 37, 123鈥?36 (2007)MATH MathSciNet
24.Winterhof, A.: Some estimates for character sums and applications. Des. Codes Cryptogr. 22(2), 123鈥?31 (2001)View Article MATH MathSciNet
25.Wu, C., Weng, X., Chen, Z.: Construction of \(k\) -ary pseudorandom elliptic curve sequences. Wuhan Univ. J. Nat. Sci. 16(5), 452鈥?56 (2011)View Article MATH MathSciNet
26.Zhang, W.: On a problem of D. H. Lehmer and its generalization. Compositio Math. 86(3), 307鈥?16 (1993)MATH MathSciNet
27.Zhang, W.: On the difference between a D. H. Lehmer number and its inverse modulo \(q\) . Acta Arith. 68(3), 255鈥?63 (1994)MATH MathSciNet
28.Zhang, W.: A problem of D. H. Lehmer and its generalization. II. Compositio Math. 91(1), 47鈥?6 (1994)MATH MathSciNet - 作者单位：Kit-Ho Mak (1)
1. School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA聽, 30332-0160, USA - 刊物主题：Mathematics, general;
- 出版者：Springer Vienna
- ISSN：1436-5081
文摘
We define the pseudorandom lattice of \(k\) symbols, and present some new constructions of families of such lattices, which generalize several previous constructions for the pseudorandom binary lattices. These lattices can also be regarded as a high dimensional analogue of some pseudorandom sequences of \(k\) symbols.