Abstract
In a series of papers Mauduit and Sárközy (partly with coauthors) studied finite pseudorandom binary sequences and they constructed sequences with strong pseudorandom properties. In these constructions fields with prime order were used. In this paper a new construction is presented, which is based on finite fields of order 2k.
Similar content being viewed by others
References
A. Sárközy, A finite pseudorandom binary sequence, Studia Sci. Math. Hungar., 38 (2001), 377–384.
J. Hoffstein and D. Lieman, The Distribution of the Quadratic Symbol in Function Fields and a Faster Mathematical Stream Cipher, Cryptography and Computational Number Theory, Progress in Computer Science and Applied Logic 20, Birkhäuser, 2001, 59–68.
E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, New York, 1968.
A. Tietäväinen, Incomplete sums and two applications of Deligne’s result, Algebra — some current trends, Lecture Notes in Math. 1352, Springer, New York, 1988, 190–205.
J. Cassaigne, C. Mauduit and A. Sárközy, On finite pseudorandom binary sequences VII: The measures of pseudorandomness, Acta Arith., 103 (2002), 97–118.
A. Reyhani-Masoleh and A. Hasan, Fast normal basis multiplication general purpose processors, IEEE Trans. Comput., 52 (2003), 1379–1390.
C. Mauduit and A. Sárközy, On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol, Acta Arith., 82 (1997), 365–377.
C. Mauduit and A. Sárközy, Construction of pseudorandom binary sequences by using the multiplicative inverse, Acta Math. Hungar., 108 (2005), 239–252.
L. Goubin, C. Mauduit and A. Sárközy, Construction of large families of pseudorandom binary sequences, J. Number Theory, 106 (2004), 56–69.
R. Ahlswede, L. Khachatrian, C. Mauduit and A. Sárközy, A complexity measure for families of binary sequences, Period. Math. Hungar., 46 (2003), 107–118.
N. Brandstätter and A. Winterhof, Linear complexity profile of binary sequences with small correlation measure, Period. Math. Hungar., 52 (2006), 1–8.
V. Tóth, Collision and avalanche effect in families of pseudorandom binary sequences, Period. Math. Hungar., 55 (2007), 185–196.
N. Brandstätter and A. Winterhof, Linear complexity profile of binary sequences with small correlation measure, Period. Math. Hungar., 52 (2006), 1–8.
K. Gyarmati, A. Sárközy and A. Pethö, On linear recursion and pseudorandomness, Acta Arith., 118 (2005), 359–374.
C. Mauduit, J. Rivat and A. Sárközy, Construction of pseudorandom Binary Sequences using additive characters, Monatsh. Math., 141 (2004), 197–208.
J. Friedlander and H. Iwaniec, Estimates for character sums, Proc. Amer. Math. Soc., 119 (1993), 365–372.
R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Mathematics 20, Cambridge University Press, 1997.
W. Schmidt, Equations over Finite Fields. An Elementary Approach, Lecture Notes in Mathematics 536, Springer, 1976.
I. M. Vinogradov, Elements of Number Theory, Dover Publications, 2003.
F. J. C. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland Mathematical Library 16, North-Holland, 1977.
J. Folláth, Construction of Pseudorandom Binary Sequences I. (2008), to appear.
J. Folláth, Construction of Pseudorandom Binary Sequences II. (2008), unpublished.
G. I. Perelprime muter, On certain character sums, Uspehi Mat. Nauk, 18 (1963), 145–149.
C. K. Caldwell, Mersenne Primes: History, Theorems and Lists, http://primes.utm.edu/mersenne/.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by András Sárközy
Rights and permissions
About this article
Cite this article
Folláth, J. Construction of pseudorandom binary sequences using additive characters over GF(2k). Period Math Hung 57, 73–81 (2008). https://doi.org/10.1007/s10998-008-7073-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10998-008-7073-1