Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Applicable Algebra in Engineering, Communication and Computing
Published in: Applicable Algebra in Engineering, Communication and Computing 2/2021

07-11-2019 | Original Paper

On the self-dual codes with an automorphism of order 5

Authors: Nikolay Yankov, Damyan Anev

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 2/2021

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

For lengths 60,  62, and 64, by applying the method for constructing self-dual codes having an automorphism of odd prime order, we classify all optimal singly even self-dual codes with an automorphism of order 5 with 12 cycles. For the binary self-dual [62, 31, 12] codes we have found five new values of the parameter in the weight enumerator thus doubling the number of know values. For length 64 we have found codes with 14 new parameter values for both known weight enumerators. By shortening all binary self-dual [60, 30, 12] codes having an automorphism of order 5 we construct many new [58, 29, 10] self-dual codes. We have found a new value of the parameter in the weight enumerator of these codes.
next article On the classification of binary self-dual codes admitting imprimitive rank 3 permutation groups

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now
Literature
1.
Yankov, N., Russeva, R.: Binary self-dual codes of lengths 52 to 60 with an automorphism of order 7 or 13. IEEE Trans. Inf. Theory 57(11), 7498–7506 (2011)MathSciNetCrossRef
2.
3.
4.
Huffman, W.C.: Automorphisms of codes with applications to extremal doubly even codes of length 48. IEEE Trans. Inf. Theory 28(3), 511–521 (1982)MathSciNetCrossRef
5.
Yorgov, V.: Binary self-dual codes with automorphisms of odd order. Probl. Inf. Transm. 19(4), 260–270 (1983)MathSciNet
6.
Yorgov, V.: A method for constructing inequivalent self-dual codes with applications to length 56. IEEE Trans. Inf. Theory 33(1), 77–82 (1987)MathSciNetCrossRef
7.
8.
Bouyukliev, I.: About the Code Equivalence in Advances in Coding Theory and Cryptography, vol. 3, pp. 126–151. World Scientific Publishing Company, Singapore (2007)CrossRef
9.
The GAP Group: GAP—Groups, Algorithms, and Programming, Version 4.8.1 (2017)
10.
Conway, J., Sloane, N.J.A.: A new upper bound on the minimal distance of self-dual codes. IEEE Trans. Inf. Theory 36(6), 1319–1333 (1990)MathSciNetCrossRef
11.
Harada, M.: Binary extremal self-dual codes of length 60 and related codes. Des. Codes Crypt. 86(5), 1085–1094 (2018)MathSciNetCrossRef
12.
Huffman, W.C., Pless, V.S.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003)CrossRef
13.
Dontcheva, R., Harada, M.: New extremal self-dual codes of length 62 and related extremal self-dual codes. IEEE Trans. Inf. Theory 48(7), 2060–2064 (2002)MathSciNetCrossRef
14.
Russeva, R., Yankov, N.: On binary self-dual codes of lengths 60, 62, 64 and 66 having an automorphism of order 9. Des. Codes Crypt. 45(3), 335–346 (2007)MathSciNetCrossRef
15.
Yankov, N.: Self-dual \([62, 31, 12]\) and \([64, 32, 12]\) codes with an automorphism of order 7. Adv. Math. Commun. 8(1), 73–81 (2014)MathSciNetCrossRef
16.
Pasquier, G.: A binary extremal doubly even self-dual code (64, 32, 12) obtained from an extended Reed–Solomon code over \(\mathbb{F}_{16}\). IEEE Trans. Inf. Theory 27(6), 807–808 (1981)CrossRef
17.
Kaya, A.: New extremal binary self-dual codes of lengths 64 and 66 from \(R_2\)-lifts. Finite Fields Appl. 46, 271–279 (2017)MathSciNetCrossRef
18.
Kaya, A., Yildiz, B., Pasa, A.: New extremal binary self-dual codes from a modified four circulant construction. Discrete Math. 339(3), 1086–1094 (2016)MathSciNetCrossRef
19.
Anev, D., Harada, M., Yankov, N.: New extremal singly even self-dual codes of lengths 64 and 66. J. Algebra Comb. Discrete Struct. Appl. 5(3), 143–151 (2018)MathSciNetMATH
20.
Gulliver, T.A., Harada, M., Kim, J.-L.: Construction of new extremal self-dual codes. Discrete Math. 263(1–3), 81–91 (2003)MathSciNetCrossRef
21.
Metadata
Title
On the self-dual codes with an automorphism of order 5
Authors
Nikolay Yankov
Damyan Anev
Publication date
07-11-2019
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 2/2021
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-019-00403-0

Other articles of this Issue 2/2021

Applicable Algebra in Engineering, Communication and Computing 2/2021 Go to the issue

Original Paper

LCD codes from weighing matrices

Original Paper

A modified Dual-Ouroboros public-key encryption using Gabidulin codes

Original Paper

Parametrization of generalized Heisenberg groups

Original Paper

On the classification of binary self-dual codes admitting imprimitive rank 3 permutation groups

Original Paper

Complexity of deciding whether a tropical linear prevariety is a tropical variety

Premium Partner

    Image Credits