Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

Published in: Applicable Algebra in Engineering, Communication and Computing 6/2021

17-03-2020 | Original Paper

On the error-detecting capability of the linear quasigroup code

Author: Natasha Ilievska

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 6/2021

Login to get access
share
SHARE

Abstract

In this paper we consider an error-detecting code based on linear quasigroups. Namely, each input block \(a_0a_1\ldots a_{n-1}\) is extended into a block \(a_0a_1\ldots a_{n-1}d_0d_1\ldots d_{n-1}\), where the redundant characters \(d_0, d_1, \ldots , d_{n-1}\) are defined with \(d_i=a_i*a_{i+1}*a_{i+2}\), where \(*\) is a linear quasigroup operation and the operations in the indexes are modulo n. We give a proof that under some conditions the code is linear. Using this fact, we contribute to the determination of the error-detecting capability of the code. Namely, we determine the Hamming distance of the code and from there we obtain the number of errors that the code will detect for sure when linear quasigroups of order 4 from the best class of quasigroups of order 4 for which the constant term in the linear representation is zero matrix are used for coding. All results in the paper are derived for arbitrary length of the input blocks. With the obtained results we showed that when a small linear quasigroup of order 4 from the best class of quasigroups of order 4 is used for coding, the number of errors that the code surely detects is upper bounded with 4.

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

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

  • über 69.000 Bücher
  • über 500 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

Testen Sie jetzt 15 Tage kostenlos.

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 58.000 Bücher
  • über 300 Zeitschriften

aus folgenden Fachgebieten:

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




Testen Sie jetzt 15 Tage kostenlos.

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 50.000 Bücher
  • über 380 Zeitschriften

aus folgenden Fachgebieten:

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




Testen Sie jetzt 15 Tage kostenlos.

Literature
1.
go back to reference Ilievska, N.: Proving the probability of undetected errors for an error-detecting code based on quasigroups. Quasigroups Relat. Syst. 22(2), 223–246 (2014) MathSciNetMATH Ilievska, N.: Proving the probability of undetected errors for an error-detecting code based on quasigroups. Quasigroups Relat. Syst. 22(2), 223–246 (2014) MathSciNetMATH
2.
go back to reference Ilievska, N., Gligoroski, D.: Error-detecting code using linear quasigroups. In: Advances in Intelligent Systems and Computing, vol. 311. Springer, pp. 309–318 (2014) Ilievska, N., Gligoroski, D.: Error-detecting code using linear quasigroups. In: Advances in Intelligent Systems and Computing, vol. 311. Springer, pp. 309–318 (2014)
3.
4.
go back to reference Ramabadran, T.V., Gaitonde, S.S.: A tutorial on CRC computations. IEEE Micro 8(4), 62–75 (1988) CrossRef Ramabadran, T.V., Gaitonde, S.S.: A tutorial on CRC computations. IEEE Micro 8(4), 62–75 (1988) CrossRef
5.
go back to reference Koopman, P., Chakravarty, T.: Cyclic redundancy code (CRC) polynomial selection for embedded networks. In: Proceedings of the International Conference on Dependable Systems and Networks, pp. 145–154 (2004) Koopman, P., Chakravarty, T.: Cyclic redundancy code (CRC) polynomial selection for embedded networks. In: Proceedings of the International Conference on Dependable Systems and Networks, pp. 145–154 (2004)
6.
go back to reference Latif-Shabgahi, G., Bass, J.M., Bennett, S.: A taxonomy for software voting algorithms used in safety-critical systems. IEEE Trans. Reliab. 53(3), 319–328 (2004) CrossRef Latif-Shabgahi, G., Bass, J.M., Bennett, S.: A taxonomy for software voting algorithms used in safety-critical systems. IEEE Trans. Reliab. 53(3), 319–328 (2004) CrossRef
7.
go back to reference Knight, J.C.: Safety critical systems: challenges and directions. In: Proceedings of the 24th International Conference on Software Engineering, pp. 547–550 (2002) Knight, J.C.: Safety critical systems: challenges and directions. In: Proceedings of the 24th International Conference on Software Engineering, pp. 547–550 (2002)
8.
go back to reference Vanstone, S., Oorschot, P.: An Introduction to Error Correcting Codes with Applications. Kluwer Academic Publishers, Boston (1989) CrossRef Vanstone, S., Oorschot, P.: An Introduction to Error Correcting Codes with Applications. Kluwer Academic Publishers, Boston (1989) CrossRef
9.
go back to reference Ilievska, N.: On the error-detection properties of the error-detecting code. In: Proceedings of the 26th Telecommunications Forum Telfor 2018, pp. 187–190 (2018) Ilievska, N.: On the error-detection properties of the error-detecting code. In: Proceedings of the 26th Telecommunications Forum Telfor 2018, pp. 187–190 (2018)
Metadata
Title
On the error-detecting capability of the linear quasigroup code
Author
Natasha Ilievska
Publication date
17-03-2020
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 6/2021
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-020-00422-2

Other articles of this Issue 6/2021

Applicable Algebra in Engineering, Communication and Computing 6/2021 Go to the issue

Premium Partner