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Cryptography and Communications

, Volume 10, Issue 4, pp 643–653 | Cite as

The symbol-pair distance distribution of a class of repeated-root cyclic codes over \(\phantom {\dot {i}\!}\mathbb {F}_{p^{m}}\)

  • Zhonghua Sun
  • Shixin Zhu
  • Liqi Wang
Article
  • 341 Downloads

Abstract

Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channel. One main task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we investigate the symbol-pair distance of cyclic codes of length p e over \(\phantom {\dot {i}\!}\mathbb {F}_{p^{m}}\). The exact symbol-pair distance of all cyclic codes of such length is determined.

Keywords

Symbol-pair codes Distance distribution Cyclic codes 

Mathematics Subject Classification (2010)

94B15 94B05 

Notes

Acknowledgments

We would like to thank the referees for their invaluable comments and a very meticulous reading of the manuscript. The research was supported in part by the National Natural Science Foundation of China under Grant Nos.61370089, 11501156 and 11626077, in part by the Fundamental Research Funds for the Central Universities under Grant Nos. JZ2015HGBZ0499, and JZ2016HGTA0708.

References

  1. 1.
    Cassuto, Y., Blaum, M.: Codes for symbol-pair read channels [C]. In: Proceedings IEEE International Symposium on Information theory, Austin, TX, USA, pp 988–992 (2010)Google Scholar
  2. 2.
    Cassuto, Y., Blaum, M.: Codes for symbol-pair read channels [J]. IEEE Trans. Inf. Theory 57(12), 8011–8020 (2011)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Cassuto, Y., Litsyn, S.: Symbol-pair codes: algebraic constructions and asymptotic bounds [C]. In: Proceedings IEEE International Symposium on Information theory, St. Petersburg, Russia, pp 2348–2352 (2011)Google Scholar
  4. 4.
    Chee, Y.M., Kiah, H.M., Wang, C.: Maximum distance separable symbol-pair codes [C]. In: Proceedings of International Symposium on Information theory, Cambridge, MA, USA, pp 2886–2890 (2012)Google Scholar
  5. 5.
    Chee, Y.M., Ji, L., Kiah, H.M., Wang, C., Yin, J.: Maximum distance separable codes for symbol-pair read channels [J]. IEEE Trans. Inf. Theory 59(11), 7259–7267 (2013)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Chen, B., Lin, L., Liu, H.: Constacyclic symbol-pair codes: lower bounds and optimal constructions [J]. arXiv:http://arxiv.org/abs/1605.03460 (2016)
  7. 7.
    Massey, J.L., Costello, D.J., Justesen, J.: Polynomial weights and code constructions [J]. IEEE Trans. Inf. Theory 19(1), 101–110 (1973)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Dinh, H.Q.: On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions [J]. Finite Fields Appl. 14(1), 22–40 (2008)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Kai, X., Zhu, S., Li, P.: A construction of new MDS Symbol-Pair codes [J]. IEEE Trans. Inf. Theory 61(11), 5828–5834 (2015)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Yaakobi, E., Bruck, J., Siegel, P.H.: Decoding of cyclic codes over symbol-pair read channels [C]. In: Proceedings of International Symposium on Information theory, Cambridge, MA, USA, pp 2891–2895 (2012)Google Scholar
  11. 11.
    Yaakobi, E., Bruck, J., Siegel, P.H.: Constructions and decoding of cyclic codes over b-symbol read channels [J]. IEEE Trans. Inf. Theory 62(4), 1541–1551 (2016)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of MathematicsHefei University of TechnologyHefeiPeople’s Republic of China

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