Have a personal or library account? Click to login
Random Polynomials in Legendre Symbol Sequences Cover

Random Polynomials in Legendre Symbol Sequences

Open Access
|Aug 2023

References

  1. ALON, N.—KOHAYAKAWA, Y.—MAUDUIT, C.—MOREIRA, C. G.—RÖDL, V.: Measures of Pseudorandomness for Finite Sequences: Minimal Values, Combin. Probab. Comput. 15 (2006), no. 1–2, 1–29.
  2. ALON, N.—KOHAYAKAWA, Y.—MAUDUIT, C.—MOREIRA, C. G.—RÖDL, V.: Measures of pseudorandomness for finite sequences: typical values, Proc. Lond. Math. Soc. 95 (2007), no. 3, 778–812.
  3. ANANTHARAM, V.: A technique to study the correlation measures of binary sequences, Discrete Math. 308 (2008), no. 24, 6203–6209.
  4. CASSAIGNE, J.—MAUDUIT, C.—SÁRKÖZY, A.: On finite pseudorandom binary sequences VII: The measures of pseudorandomness, Acta Arith. 103 (2001), no. 2, 97–118.
  5. GOUBIN, L.—MAUDUIT, C.—SÁRKÖZY, A.: Construction of large families of pseudorandom binary sequences, J. Number Theory 106 (2004), no. 1, 56–69.
  6. GYARMATI, K.: On the correlation of binary sequences, Studia Sci. Math. Hungar. 42 (2005), 59–75.
  7. GYARMATI, K.: Measures of pseudorandomness. In: Finite fields and their applications, (P. Charpin, A. Pott, A. Winterhof, eds.), Radon Ser. Comput. Appl. Math. Vol. 11, De Gruyter, Berlin, 2013. pp. 43–64.
  8. GYARMATI, K.—MAUDUIT, C.: On the correlation of binary sequences, II, Discrete Math. 312 (2012), 811–818.
  9. HOFFSTEIN, J.—LIEMAN, D.: The distribution of the quadratic symbol in function fields and a faster mathematical stream cipher. In: (Lam, Kwok-Yan et al. ed.) Cryptography and Computational Number Theory (Singapore, November 22–26, 1999), Prog. Comput. Sci. Appl. Log. Vol. 20, Birkhäuser, Basel, 2001, pp. 59–68.
  10. MATLAB version 9.7.0. Natick, Massachusetts: The MathWorks Inc. 2018.
  11. MAUDUIT, C.—SÁRKÖZY, A.: On finite pseudorandom binary sequences, I. Measures of pseudorandomness, the Legendre symbol, Acta Arith. 82 (1997), no. 4, 365–377.
  12. MÜLLNER, K.: MATLAB code for find a quadratic non-residue n which is admissible to f(x) https://github.com/mullni/mycodes/blob/main/ottis.m
  13. STRANDMARK, P.: MATLAB code for computes the Jacobi symbol, a generalization of the Legendre symbol https://github.com/mullni/mycodes/blob/main/jacobi.m
  14. WEIL, A.: Sur les courbes algébriques et les variétés qui s’en déduisent, Actualités Scientifiques et Industrielles. No. 1041; Publ. Inst. Math. Univ. Strasbourg, 7 (1945). Act. Sci. Ind. [Current Scientific and Industrial Topics], Vol. 1041, Hermann & Cie, Paris, 1948, iv+85 pp.
DOI: https://doi.org/10.2478/udt-2023-0006 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Language: English
Page range: 83 - 96
Submitted on: Apr 14, 2023
Accepted on: Apr 25, 2023
Published on: Aug 10, 2023
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2023 Katalin Gyarmati, Károly Müllner, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.