nach oben

Cryptography and Communications

Erschienen in:

25.07.2016

Two classes of p-ary bent functions and linear codes with three or four weights

verfasst von: Guangkui Xu, Xiwang Cao, Shanding Xu

Erschienen in: Cryptography and Communications | Ausgabe 1/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper, a secondary construction of p-ary bent functions is presented. Two classes of p-ary bent functions of algebraic degree p are constructed by modifying the values of some known bent functions on some set of \(\mathbb {F}_{p^{2k}}\). Furthermore, the resulted p-ary bent functions are employed to construct a class of linear codes with three or four weights.

Vorheriger Artikel A class of linear codes with a few weights

Nächster Artikel A class of three-weight linear codes and their complete weight enumerators

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

Bae, S., Li, C., Yue, Q.: Some results on two-weight and three-weight linear codes preprint, 2015.

Carlet, C.: Two New Classes of Bent Functions. Advances in Cryptology-EUROCRYPT93, Springer, Pp. 77–101 (1994).

Carlet, C.: On Bent and Highly Nonlinear Balanced/Resilient Functions and Their Algebraic Immunities. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Springer, Pp. 1–28 (2006).

Carlet, C.: Boolean functions for cryptography and error correcting codes. Boolean Models and Methods in Mathematics. Comput. Sci. Eng. 2, 257–397 (2010).MATH

Carlet, C., Mesnager, S.: On Dillon’s class \(\mathcal {H}\) of bent functions, Niho bent functions and o-polynomials. J. Combin. Theory Ser A. 118 (8), 2392–2410 (2011).MathSciNetCrossRefMATH

Chee, Y. M., Tan, Y., Zhang, X. D.: Strongly regular graphs constructed from p-ary bent functions. J. Algebr. Comb. 34 (2), 251–266 (2011).MathSciNetCrossRefMATH

Dillon, J. F.: Elementary hadamard difference sets, Ph.D. thesis, University of Maryland College Park, 1974.

Ding, C., Wang, X.: A coding theory construction of new systematic authentication codes. Theoretical Comput. Sci. 330 (1), 81–99 (2005).MathSciNetCrossRefMATH

Ding, C., Luo, J., Niederreiter, H.: Two Weight Codes Punctured from Irreducible Cyclic Codes. Proc. of the First International Workshop on Coding Theory and Cryptography, Singapore, World Scientific, 119-124 (2008).

Ding, C.: Linear codes from some 2-designs. IEEE Trans. Inform. Theory. 61 (6), 3265–3275 (2015).MathSciNetCrossRef

Ding, C., Li, C., Li, N., Zhou, Z.: Three-weight cyclic codes and their weight distributions. Discret. Math. 339, 415–427 (2016).MathSciNetCrossRefMATH

Ding, C.: A construction of binary linear codes from Boolean functions. Discret. Math. 339 (9), 2288–2303 (2016).MathSciNetCrossRefMATH

Ding, K., Ding, C.: Binary linear codes with three weights. IEEE Trans. Inform. Theory. 18 (11), 1879–1882 (2014).MATH

Ding, K., Ding, C.: A class of two-weight and three-weight codes and their applications in secret sharing. IEEE Trans. Inf. Theory. 61 (11), 5835–5842 (2015).MathSciNetCrossRef

Ding, C., Niederreiter, H.: Cyclotomic linear codes of order 3. IEEE Trans. Inf. Theory. 53 (6), 2274–2277 (2007).MathSciNetCrossRefMATH

Helleseth, T., Kholosha, A.: Monomial and quadratic bent functions over the finite fields of odd characteristic. IEEE Trans. Inf. Theory. 52 (5), 2018–2032 (2006).MathSciNetCrossRefMATH

Helleseth, T., Kholosha, A.: New binomial bent functions over the finite fields of odd characteristic. IEEE Trans. Inf. Theory. 56 (9), 4646–4652 (2010).MathSciNetCrossRef

Heng, Z., Yue, Q.: A class of binary linear codes with at most three weights. IEEE Commun. Lett. 19 (9), 1488–1491 (2015).CrossRef

Heng, Z., Yue, Q.: Two classes of two-weight linear codes. Finite Fields Appl. 38, 72–92 (2016).MathSciNetCrossRefMATH

Hou, X.: D.: p-Ary and q-ary versions of certain results about bent functions and resilient functions. Finite Fields Appl. 10 (4), 566–582 (2004).MathSciNetCrossRefMATH

Huffman, W. C., Pless, V.: Fundamentals of Error-Correcting codes cambridge, U.K.: Cambridge univ press, 2003.

Jia, W., Zeng, X., Helleseth, T., Li, C.: A class of binomial bent functions over the finite fields of odd characteristic. IEEE Trans. Inf. Theory. 58 (9), 6054–6063 (2012).MathSciNetCrossRef

Kumar, P. V., Scholtz, R. A., Welch, L. R.: Generalized bent functions and their properties. J. Combin. Theory Ser A. 40 (1), 90–107 (1985).MathSciNetCrossRefMATH

Li, C., Yue, Q.: A class of cyclic codes from two distinct fnite felds codes. Finite Fields Appl. 34 (2), 305–316 (2015).MathSciNetCrossRefMATH

Li, C., Yue, Q., Li, F.: Hamming weights of the duals of cyclic codes with two zeros. IEEE Trans. Inf. Theory. 60 (7), 3895–3902 (2014).MathSciNetCrossRef

Li, N., Helleseth, T., Tang, X., Kholosha, A.: Several new classes of bent functions from Dillon exponents. IEEE Trans. Inf. Theory. 59 (3), 1818–1831 (2013).MathSciNetCrossRef

Lidl, R., Niederrreiter, H.: Finite Fields. Addison-Wesley, London (1983).

Mesnager, S.: Several new infinite families of bent functions and their duals. IEEE Trans. Inf. Theory. 60 (7), 4397–4407 (2014).MathSciNetCrossRef

Mesnager, S.: Bent functions: fundamentals and results. Springer, New York. to appear.

Rothaus, O. S.: On bent functions. J. Combin. Theory Ser A. 20 (3), 300–305 (1976).MathSciNetCrossRefMATH

Tan, Y., Pott, A., Feng, T.: Strongly regular graphs associated with ternary bent functions. J. Combin. Theory Ser A. 117 (6), 668–682 (2010).MathSciNetCrossRefMATH

Tang, C., Li, N., Qi, F., Zhou, Z., Helleseth, T.: Linear codes with two or three weights from weakly regular bent functions. IEEE Trans. Inf. Theory. 62 (3), 1166–1176 (2016).MathSciNetCrossRef

Xiang, C.: Linear codes from a generic construction. Cryptogr. Commun. (2015). doi:10.1007/s12095-015-0158-1.

Xu, G., Cao, X., Xu, S.: Constructing new APN functions and bent functions over finite fields of odd characteristic via the switching method. Cryptogr Commun. 8 (1), 155–171 (2016).MathSciNetCrossRefMATH

Yuan, J., Carlet, C., Ding, C.: The weight distribution of a class of linear codes from perfect nonlinear functions. IEEE Trans. Inf. Theory. 52 (2), 712–717 (2006).MathSciNetCrossRefMATH

Zeng, X., Hu, L., Jiang, W., Yue, Q., Cao, X.: The weight distribution of a class of p-ary cyclic codes. Finite Fields Appl. 16 (1), 56–73 (2010).MathSciNetCrossRefMATH

Zhou, Z., Ding, C.: A class of three-weight cyclic codes. Finite Fields Appl. 25, 79–93 (2014).MathSciNetCrossRefMATH

Zhou, Z., Li, N., Fan, C., Helleseth, T.: Linear codes with two or three weights from quadratic bent functions. Des. Codes Cryptogr. (2015). doi:10.1007/s10623-015-0144-9.

Titel: Two classes of p-ary bent functions and linear codes with three or four weights
verfasst von: Guangkui Xu
Xiwang Cao
Shanding Xu
Publikationsdatum: 25.07.2016
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 1/2017
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-016-0199-0

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 1/2017

A class of linear codes with a few weights

Optimal codebooks achieving the Levenshtein bound from generalized bent functions over

Some cyclic codes with prime length from cyclotomy of order 4

Bent functions linear on elements of some classical spreads and presemifields spreads

A class of three-weight linear codes and their complete weight enumerators

Complete weight enumerators of some linear codes from quadratic forms