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Designs, Codes and Cryptography

Erschienen in:

19.12.2016

Nonexistence of two classes of generalized bent functions

verfasst von: Jianing Li, Yingpu Deng

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2017

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We obtain some new nonexistence results of generalized bent functions from \({\mathbb {Z}}^n_q\) to \({\mathbb {Z}}_q\) (called type [n, q]) in the case that there exist cyclotomic integers in \( {\mathbb {Z}}[\zeta _{q}]\) with absolute value \(q^{\frac{n}{2}}\). This result generalizes two previous nonexistence results \([n,q]=[1,2\times 7]\) of Pei (Lect Notes Pure Appl Math 141:165–172, 1993) and \([3,2\times 23^e]\) of Jiang and Deng (Des Codes Cryptogr 75:375–385, 2015). We also remark that by using a same method one can get similar nonexistence results of GBFs from \({\mathbb {Z}}^n_2\) to \({\mathbb {Z}}_m\).

Vorheriger Artikel Strongly regular graphs from classical generalized quadrangles

Nächster Artikel Consolidation for compact constraints and Kendall tau LP decodable permutation codes

Dillon J.F.: Elementary Hadamard difference sets. PhD dissertation, University of Maryland (1974).

Feng K.: Generalized bent functions and class group of imaginary quadratic fields. Sci China Ser. A 44, 562–570 (2001).MathSciNetCrossRefMATH

Feng K., Liu F.: New results on the nonexistence of generalized bent functions. IEEE Trans. Inf. Theory 49, 3066–3071 (2003).MathSciNetCrossRefMATH

Feng K., Liu F.: Non-existence of some generalized bent functions. Acta Math. Sin. (Engl. Ser.) 19, 39–50 (2003).MathSciNetCrossRefMATH

Francois D.G., Dominic K.: A Wieferich prime search up to \(6.7 \times 10^{15}\). J. Integer Seq. 14, 1–14 (2011).MATH

Fröhlich A., Taylor M.J.: Algebraic Number Theory. Cambridge University Press, Cambridge (1991).CrossRefMATH

Ikeda M.: A remark on the non-existence of generalized bent functions. Lect. Notes Pure Appl. Math. 204, 109–119 (1999).MathSciNetMATH

Jiang Y., Deng Y.: New results on nonexistence of generalized bent functions. Des. Codes Cryptogr. 75, 375–385 (2015).MathSciNetCrossRefMATH

Kumar P.V., Scholtz R.A., Welch L.R.: Generalized bent functions and their properties. J. Comb. Theory Ser. A 40, 90–107 (1985).MathSciNetCrossRefMATH

10.

Liu H., Feng K., Feng R.: Nonexistence of generalized bent functions from \(\mathbb{Z}_{2}^{n}\) to \(\mathbb{Z}_{m}\). Des. Codes Cryptogr. (2016). doi:10.1007/s10623-016-0192-9.

11.

Logachev O.A., Salnikov A.A., Yashchenko V.V.: Bent functions over a finite abelian group. Discret. Math. Appl. 7, 547–564 (1997).CrossRefMATH

12.

Marcus D.A.: Number Fields. Springer, Berlin (1997).

13.

Olsen J.D., Scholtz R.A., Welch L.R.: Bent-function sequences. IEEE Trans. Inf. Theory 28, 858–864 (1982).MathSciNetCrossRefMATH

14.

Pei D.: On nonexistence of generalized bent functions. Lect. Notes Pure Appl. Math. 141, 165–172 (1993).MathSciNetMATH

15.

Poinsot L.: Bent functions on a finite nonabelian group. J. Discret. Math. Sci. Cryptogr. 9, 349–364 (2006).MathSciNetCrossRefMATH

16.

Rothaus O.S.: On “bent” functions. J. Comb. Theory. A 20, 300–305 (1976).CrossRefMATH

17.

Solodovnikov V.I.: Bent functions from a finite abelian group to a finite abelian group. Diskret. Mat. 14, 99–113 (2002).MathSciNetCrossRefMATH

18.

Stănică P., Martinsen T., Gangopadhyay S., Brajesh K.S.: Bent and generalized bent Boolean functions. Des. Codes Cryptogr. 69, 77–94 (2013).MathSciNetCrossRefMATH

19.

Washington L.C.: Introduction to Cyclotomic Fields, 2nd edn. Graduate Texts in Mathematics. Springer, New York (1997).

20.

Xu B.: Bentless and nonlinearity of functions on finite groups. Des. Codes Cryptogr. (2014). doi:10.1007/s10623-014-9968-y.

Titel: Nonexistence of two classes of generalized bent functions
verfasst von: Jianing Li
Yingpu Deng
Publikationsdatum: 19.12.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2017
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-016-0319-z

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