nach oben

Cryptography and Communications

Erschienen in:

21.04.2016

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

verfasst von: Shudi Yang, Zheng-An Yao, Chang-An Zhao

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

Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime p, we propose a class of p-ary linear codes by choosing a proper defining set. Their weight enumerators and complete weight enumerators are presented explicitly. Our results show that they are linear codes with three weights and suitable for the constructions of authentication codes and secret sharing schemes.

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

Nächster Artikel Complete weight enumerators of some linear codes from quadratic forms

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

Ahn, J., Ka, D., Li, C.: Complete weight enumerators of a class of linear codes, preprint (2016)

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

Berndt, B.C., Evans, R.J., Williams, K.S.: Gauss and Jacobi Sums. Wiley, New York (1998)MATH

Blake, I.F., Kith, K.: On the complete weight enumerator of Reed-Solomon codes. SIAM J. Discret. Math. 4(2), 164–171 (1991)MathSciNetCrossRefMATH

Carlet, C., Ding, C., Yuan, J.: Linear codes from perfect nonlinear mappings and their secret sharing schemes. IEEE Trans. Inf. Theory 51(6), 2089–2102 (2005)MathSciNetCrossRefMATH

Chu, W., Colbourn, C.J., Dukes, P.: On constant composition codes. Discret. Appl. Math. 154(6), 912–929 (2006)MathSciNetCrossRefMATH

Ding, C.: Optimal constant composition codes from zero-difference balanced functions. IEEE Trans. Inf. Theory 54(12), 5766–5770 (2008)MathSciNetCrossRefMATH

Ding, C.: Codes from Difference Sets. World Scientific, Singapore (2015)

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

10.

Ding, C., Helleseth, T., Klove, T., Wang, X.: A generic construction of Cartesian authentication codes. IEEE Trans. Inf. Theory 53(6), 2229–2235 (2007)MathSciNetCrossRefMATH

11.

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

12.

Ding, C., Yang, J.: Hamming weights in irreducible cyclic codes. Discret. Math. 313(4), 434–446 (2013)MathSciNetCrossRefMATH

13.

Ding, C., Yin, J.: A construction of optimal constant composition codes. Des. Codes Crypt. 40(2), 157–165 (2006)MathSciNetCrossRefMATH

14.

Ding, K., Ding, C.: Binary linear codes with three weights. IEEE Commun. Lett. 18(11), 1879–1882 (2014)CrossRefMATH

15.

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

16.

Dinh, H.Q., Li, C., Yue, Q.: Recent progress on weight distributions of cyclic codes over finite fields. J. Algebra Comb. Discret. Struct. Appl. 2(1), 39–63 (2015)MathSciNetMATH

17.

Feng, K., Luo, J.: Weight distribution of some reducible cyclic codes. Finite Fields Appl. 14(2), 390–409 (2008)MathSciNetCrossRefMATH

18.

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

19.

Heng, Z., Yue, Q.: Complete weight distributions of two classes of cyclic codes. Cryptogr. Commun. (2016). doi:10.1007/s12095-015-0177-y MATH

20.

Kith, K.: Complete weight enumeration of Reed-Solomon codes. Master’s thesis, Department of Electrical and Computing Engineering, University of Waterloo, Waterloo (1989)

21.

Kuzmin, A., Nechaev, A.: Complete weight enumerators of generalized Kerdock code and linear recursive codes over Galois ring. In: Workshop on coding and cryptography, pp. 333–336 (1999)

22.

Kuzmin, A., Nechaev, A.: Complete weight enumerators of generalized Kerdock code and related linear codes over Galois ring. Discret. Appl. Math. 111(1), 117–137 (2001)MathSciNetCrossRefMATH

23.

Li, C., Bae, S., Ahn, J., Yang, S., Yao, Z.A.: Complete weight enumerators of some linear codes and their applications. Des. Codes Crypt. (2015). doi:10.1007/s10623-015-0136-9 MathSciNetMATH

24.

Li, C., Yue, Q., Fu, F.W.: Complete weight enumerators of some cyclic codes. Des. Codes Crypt. (2015). doi:10.1007/s10623-015-0091-5 MathSciNetMATH

25.

Lidl, R., Niederreiter, H.: Finite Fields. Encyclopedia of Mathematics and Its Applications, vol. 20. Addison-Wesley, Reading (1983)MATH

26.

Luo, J., Feng, K.: On the weight distributions of two classes of cyclic codes. IEEE Trans. Inf. Theory 54(12), 5332–5344 (2008)MathSciNetCrossRefMATH

27.

MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes, vol. 16. North-Holland Publishing, Amsterdam (1977)

28.

Myerson, G.: Period polynomials and Gauss sums for finite fields. Acta Arith. 39(3), 251–264 (1981)MathSciNetMATH

29.

Sharma, A., Bakshi, G.K.: The weight distribution of some irreducible cyclic codes. Finite Fields Appl. 18(1), 144–159 (2012)MathSciNetCrossRefMATH

30.

Tang, C., Li, N., Qi, Y., 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

31.

Vega, G.: The weight distribution of an extended class of reducible cyclic codes. IEEE Trans. Inf. Theory 58(7), 4862–4869 (2012)MathSciNetCrossRef

32.

Wang, B., Tang, C., Qi, Y., Yang, Y., Xu, M.: The weight distributions of cyclic codes and elliptic curves. IEEE Trans. Inf. Theory 58(12), 7253–7259 (2012)MathSciNetCrossRef

33.

Wang, Q., Li, F., Ding, K., Lin, D.: Complete weight enumerators of two classes of linear codes. arXiv:1512.07341 (2015)

34.

Yang, S., Yao, Z.A.: Complete weight enumerators of a family of three-weight linear codes. Des. Codes Crypt. (2016). doi:10.1007/s10623-016-0191-x

35.

Yu, L., Liu, H.: The weight distribution of a family of p-ary cyclic codes. Des. Codes Crypt. (2014). doi:10.1007/s10623-014-0029-3

36.

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

37.

Zheng, D., Wang, X., Yu, L., Liu, H.: The weight enumerators of several classes of p-ary cyclic codes. Discret. Math. 338(7), 1264–1276 (2015)MathSciNetCrossRefMATH

38.

Zhou, Z., Ding, C., Luo, J., Zhang, A.: A family of five-weight cyclic codes and their weight enumerators. IEEE Trans. Inf. Theory 59(10), 6674–6682 (2013)MathSciNetCrossRef

Titel: A class of three-weight linear codes and their complete weight enumerators
verfasst von: Shudi Yang
Zheng-An Yao
Chang-An Zhao
Publikationsdatum: 21.04.2016
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/s12095-016-0187-4

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

Linear codes with few weights from weakly regular bent functions based on a generic construction

Preface: Special functions and codes

A construction of codes with linearity from two linear codes

Some cyclic codes with prime length from cyclotomy of order 4

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

A class of linear codes with a few weights