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 5/2016

25-02-2016 | Original Paper

Constructions of self-dual codes and formally self-dual codes over rings

Authors: Steven T Dougherty, Abidin Kaya, Esengül Saltürk

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 5/2016

Log in

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

search-config
loading …

Abstract

We shall describe several families of X-rings and construct self-dual and formally self-dual codes over these rings. We then use a Gray map to construct binary formally self-dual codes from these codes. In several cases, we produce binary formally self-dual codes with larger minimum distances than known self-dual codes. We also produce non-linear codes which are better than the best known linear codes.
previous article New secondary constructions of Bent functions

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.
Batoul, A., Guenda, K., Kaya, A., Yildiz, B.: Cyclic isodual and formally self-dual codes over \({\mathbb{F}}_{q}+v{\mathbb{F}}_{q}\). Eur. J. Pure Appl. Math. 8(1), 64–80 (2015)MathSciNet
2.
Calderbank, A.R., Hammons, A.R., Kumar, P.V., Sloane, N.J.A., Solé, P.: A linear construction for certain Kerdock and Preparata codes. Bull. Am. Math. Soc. 29(2), 218–222 (1993)MathSciNetCrossRefMATH
3.
Dougherty, S.T., Salturk, E., Szabo, S.: Codes over local rings of order \(16\) and binary codes, to appear in Adv. Math. Comm
4.
Dougherty, S.T., Salturk, E.: Codes over local rings, gray maps and self-dual codes, in submission
5.
Dougherty, S.T., Yildiz, B., Karadeniz, S.: Codes over \(R_k\), gray maps and their binary images. Finite Fields Appl. 17(3), 205–219 (2011)MathSciNetCrossRefMATH
6.
Dougherty, S.T., Yildiz, B., Karadeniz, S.: Self-dual codes over \(R_{k}\) and binary self-dual codes. Eur. J. Pure Appl. Math. 6(1), 89–106 (2013)MathSciNetMATH
7.
8.
Karadeniz, S., Yildiz, B.: Double-circulant and bordered-double-circulant constructions for self-dual codes over \(R_{2}\), Adv. Math. Commun. 6(2), 193–202 (2012)MathSciNetCrossRefMATH
9.
Karadeniz, S., Dougherty, S.T., Yildiz, B.: Constructing formally self-dual codes over \(R_{k}\). Discrete Appl. Math. 167, 188–196 (2014)MathSciNetCrossRefMATH
10.
Moro, E.M., Szabo, S., Yildiz, B.: Linear codes over \({\mathbb{Z}} _{4}\left[x\right] /\left\langle x^{2}+2x\right\rangle \). Int. J. Inf. Coding Theory 3(1), 78–96 (2015)MathSciNetCrossRef
Metadata
Title
Constructions of self-dual codes and formally self-dual codes over rings
Authors
Steven T Dougherty
Abidin Kaya
Esengül Saltürk
Publication date
25-02-2016
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 5/2016
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-016-0288-5

Other articles of this Issue 5/2016

Applicable Algebra in Engineering, Communication and Computing 5/2016 Go to the issue

Original Paper

New secondary constructions of Bent functions

Original Paper

Trisection for genus 2 curves in odd characteristic

Original Paper

On weak differential uniformity of vectorial Boolean functions as a cryptographic criterion

Original Paper

Partial permutation decoding for MacDonald codes

Premium Partner

    Image Credits