Abstract
Symbol-pair codes, introduced by Cassuto and Blaum (Proc IEEE Int Symp Inf Theory, 988–992, 2010 [1]), have been raised for symbol-pair read channels. This new idea is motivated by the limitations of the reading process in high-density data storage technologies. Yaakobi et al. (IEEE Trans Inf Theory 62(4):1541–1551, 2016 [8]) introduced codes for b-symbol read channels, where the read operation is performed as a consecutive sequence of \(b>2\) symbols. In this paper, we come up with a method to compute the b-symbol-pair distance of two n-tuples, where n is a positive integer. Also, we deal with the b-symbol-pair distances of some kind of cyclic codes of length \(p^e\) over \({F}_{p^m}\).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cassuto, Y., Blaum. M.: Codes for symbol-pair read channels. In: Proceeding of the IEEE International Symposium on Information Theory, Austin, TX, USA, June, pp. 988–992. (2010)
Cassuto, Y., Blaum, M.: Codes for symbol-pair read channels. IEEE Trans. Inf. Theory 57(12), 8011–8020 (2011)
Cassuto, Y., Litsyn, Y.: Symbol-pair codes: algebraic constructions and asymptotic bounds. In: Proceeding of the IEEE International Symposium on Information Theory, St. Petersburg, Russia, July/Aug, pp. 2348–2352. (2011)
Chee, Y.M., Ji, L., Kiah, H.M., Wang, C., Yin, J.: Maximum distance separable codes for symbol-pair read channels. IEEE Trans. Inf. Theory 59(11), 7259–7267 (2013)
Chee, Y.M., Kiah, H.M., Wang, C.: Maximum distance separable symbol-pair codes. In: Proceeding of the International Symposium on Information Theory, Cambridge, MA, USA, July, pp. 2886–2890. (2012)
Dinh, H.Q.: On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions. Finite Fields Appl. 14(1), 22–40 (2008)
Hirotomo, M., Takita, M., Morii, M.: Syndrome decoding of symbol-pair codes. In: Proceeding of the IEEE Information Theory Workshop, Hobart, TAS, Australia, pp. 162–166. (2014)
Yaakobi, E., Bruck, J., Siegel, P.H.: Constructions and decoding of cyclic codes over \(b\)-symbol read channels. IEEE Trans. Inf. Theory 62(4), 1541–1551 (2016)
Yaakobi, E., Bruck, J., Siegel, P.H.: Decoding of cyclic codes over symbol-pair read channels. In: Proceeding of the International Symposium on Information Theory, Cambridge, MA, USA, pp. 2891–2895. (2012)
Zhu, S., Sun, Z., Wang, L.: The symbol-pair distance distribution of repeated-root cyclic codes over \({F}_{p^m}\). arXiv:1607.01887v1, (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Mostafanasab, H., Sevim, E.S. (2018). b-Symbol Distance Distribution of Repeated-Root Cyclic Codes. In: Badawi, A., Vedadi, M., Yassemi, S., Yousefian Darani, A. (eds) Homological and Combinatorial Methods in Algebra. SAA 2016. Springer Proceedings in Mathematics & Statistics, vol 228. Springer, Cham. https://doi.org/10.1007/978-3-319-74195-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-74195-6_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-74194-9
Online ISBN: 978-3-319-74195-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)