nach oben

Cryptography and Communications

Erschienen in:

01.06.2021

A family of optimal ternary cyclic codes with minimum distance five and their duals

verfasst von: Dandan Wang, Xiwang Cao

Erschienen in: Cryptography and Communications | Ausgabe 1/2022

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

As a subclass of linear codes, cyclic codes have important applications in consumer electronics, data storage systems and communication systems. In this paper, a new family of optimal ternary cyclic codes with minimum distance five are obtained from known perfect nonlinear functions over \(\mathbb {F}_{3^{m}}\). Moreover, we investigate the weight distributions of their duals.

Nächster Artikel New constructions of entanglement-assisted quantum codes

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

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

Chien, R.T.: Cyclic decoding procedure for Bose-Chaudhuri-Hocquenghem codes. IEEE Trans. Inf. Theory. 10(4), 357–363 (1964)CrossRef

Coulter, R.S.: The number of rational points of a class of Artin-Schreier curves. Finite Fields Appl. 8(4), 397–413 (2002)MathSciNetCrossRef

Coulter, R.S.: Explicit evaluations of some Weil sums. Acta Arithmetica. 83, 241–251 (1998)MathSciNetCrossRef

Delsarte, P.: On subfield subcodes of modified Reed-Solomon codes. IEEE Trans. Inf. Theory. 21(5), 575–576 (1975)MathSciNetCrossRef

Ding, C., Helleseth, T.: Optimal ternary cyclic codes from monomials. IEEE Trans. Inf. Theory. 59(9), 5898–5904 (2013)MathSciNetCrossRef

Fan, C., Li, N., Zhou, Z.: A class of optimal ternary cyclic codes and their duals. Finite Fields Appl. 37, 193–202 (2016)MathSciNetCrossRef

Hu, H., Zhang, Q., Shao, S.: On the dual of the Coulter-Matthews bent functions. IEEE Trans. Inf. Theory 63(4), 2454–2463 (2017)MathSciNetCrossRef

Hu, H., Yang, X., Tang, S.: New classes of ternary bent functions from the Coulter-Matthews bent functions. IEEE Trans. Inf. Theory 646, 4653–4663 (2018)MathSciNetCrossRef

10.

Feng, K., Luo, J.: Value distributions of exponential sums from perfect nonlinear functions and their applications. IEEE Trans. Inf. Theory 53(9), 3035–3041 (2007)MathSciNetCrossRef

11.

Forney, G.D.: On decoding BCH codes. IEEE Trans. Inf. Theory. 11(4), 549–337 (1995)MathSciNetCrossRef

12.

Huffman, W.C., Pless, V.: Fundamentals of Error-Correcting Codes. Cambridge Univ. Press, Cambrige, U. K. (2003)CrossRef

13.

Li, N., Li, C., Helleseth, T., Ding, C., Tang, X.: Optimal ternary cyclic codes with minimum distance four and five. Finite Fields Appl. 30, 100–120 (2014)MathSciNetCrossRef

14.

Li, N., Zhou, Z., Helleseth, T.: On a conjecture about a class of optimal ternary cyclic codes. In: Seventh International Workshop on Signal Design and its Applications in Communications (IWSDA). https://doi.org/10.1109/IWSDA.2015.7458415 (2015)

15.

Lidl, R., Niederreiter, H.: Finite Field. Cambridge University Press, Cambridge (1997)MATH

16.

Liu, Y., Cao, X., Lu, W.: On some conjectures about optimal ternary cyclic codes. Des. Codes Crypt. 88, 297–309 (2020)MathSciNetCrossRef

17.

Liu Y., Cao, X: Four classes of optimal quinary cyclic codes. IEEE Comm. Letters. https://doi.org/10.1109/LCOMM.2020.2983373 (2020)

18.

Luo, J., Feng, K.: Cyclic codes and sequences from generalized Coulter-Matthews function. IEEE Trans. Inf. Theory. 54(12), 5345–5353 (2008)MathSciNetCrossRef

19.

Prange, E.: Some cyclic error-correcting codes with simple decoding algorithms Cambridge. MA, USA Air Force Cambridge Research Center-TN-58-156 (1958)

20.

Rouayheb, S.Y.E.I., Georghiaheds, C.N., Soljanin, E., Sprintson, A.: Bounds on codes based on graph theory. IEEE Int. Symp. Inform. Theory. pp. 1876–1879 (2007)

21.

Schmidt, B., White, C.: All two-weight irreducible cyclic codes. Finite Fields Appl. 8(1), 1–17 (2002)MathSciNetCrossRef

22.

Wang, L., Wu, G.: Several classes of optimal ternary cyclic codes with minimal distance four. Finite Fields Appl. 40, 126–137 (2016)MathSciNetCrossRef

23.

Xu, G., Cao, X., Xu, S.: Optimal p-ary cyclic codes with minimum distance four from monomials. Crypt. Commun. 8(4), 541–554 (2016)MathSciNetCrossRef

24.

Yan, H., Zhou, Z., Du, X.: A family of optimal ternary cyclic codes from Niho-type exponent. Finite Fiels Appl. 54, 101–112 (2018)MathSciNetCrossRef

25.

Zheng, D., Wang, X., Hu, L., Zeng, X.: The weight distributions of two classes of p-ary cyclic codes. Finite Fields Appl. 29, 202–224 (2014)MathSciNetCrossRef

26.

Zheng, D., Wang, X., Zeng, X., Hu, L.: The weight distribution of a family of p-ary cyclic codes. Des. Codes Crypt. 75(2), 263–275 (2015)MathSciNetCrossRef

27.

Zha, Z., Hu, L.: New classes of optimal ternary cyclic codes with minimum distance four. Finite Fields Appl. 64, 101671 (2020)MathSciNetCrossRef

28.

Zhou, Z., Ding, C.: A class of three-weight cyclic codes. Finite Fields Appl. 25(10), 79–93 (2013)MathSciNetMATH

29.

Zhou, Z., Ding, C.: Seven classes of three-weight cyclic codes. IEEE Trans. Inf. Theory. 61(10), 4120–4126 (2013)

30.

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 family of optimal ternary cyclic codes with minimum distance five and their duals
verfasst von: Dandan Wang
Xiwang Cao
Publikationsdatum: 01.06.2021
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 1/2022
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-021-00493-z

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 1/2022

New constant dimension subspace codes from block inserting constructions

Preimages of p −Linearized Polynomials over

Construction of LCD and new quantum codes from cyclic codes over a finite non-chain ring

Permutations without linear structures inducing bent functions outside the completed Maiorana-McFarland class

A new family of polyphase sequences with low correlation

New constructions of entanglement-assisted quantum codes

Premium Partner