Random Polynomials in Legendre Symbol Sequences

[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. Search in Google Scholar

[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. Search in Google Scholar

[3] ANANTHARAM, V.: A technique to study the correlation measures of binary sequences, Discrete Math. 308 (2008), no. 24, 6203–6209. Search in Google Scholar

[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. Search in Google Scholar

[5] GOUBIN, L.—MAUDUIT, C.—SÁRKÖZY, A.: Construction of large families of pseudorandom binary sequences, J. Number Theory 106 (2004), no. 1, 56–69. Search in Google Scholar

[6] GYARMATI, K.: On the correlation of binary sequences, Studia Sci. Math. Hungar. 42 (2005), 59–75. Search in Google Scholar

[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. Search in Google Scholar

[8] GYARMATI, K.—MAUDUIT, C.: On the correlation of binary sequences, II, Discrete Math. 312 (2012), 811–818. Search in Google Scholar

[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. Search in Google Scholar

[10] MATLAB version 9.7.0. Natick, Massachusetts: The MathWorks Inc. 2018. Search in Google Scholar

[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. Search in Google Scholar

[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 Search in Google Scholar

[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 Search in Google Scholar

[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. Search in Google Scholar