Share This Article:

Images of Linear Block Codes over Fq+uFq+vFq+uvFq

Abstract Full-Text HTML Download Download as PDF (Size:1028KB) PP. 27-31
DOI: 10.4236/ojapps.2013.31B1006    2,962 Downloads   4,908 Views   Citations

ABSTRACT

In this paper, we considered linear block codes over Rq=Fq+uFq+vFq+uvFq, u2=v2=0,uv=vu where q=pm, m∈N . First we looked at the structure of the ring. It was shown that Rq is neither a finite chain ring nor a principal ideal ring but is a local ring. We then established a generator matrix for the linear block codes and equipped it with a homogeneous weight function. Field codes were then constructed as images of these codes by using a basis of Rq over Fq . Bounds on the minimum Hamming distance of the image codes were then derived. A code meeting such bounds is given as an example.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

J. Palacio and V. Sison, "Images of Linear Block Codes over Fq+uFq+vFq+uvFq," Open Journal of Applied Sciences, Vol. 3 No. 1B, 2013, pp. 27-31. doi: 10.4236/ojapps.2013.31B1006.

References

[1] S. T. Dougherty, M. K. Gupta and K. Shiromoto, “On Generalized Weights for Codes over Finite Rings,” pre-print, 2002.
[2] T. Honold, “A Characterization of Finite Frobenius Rings,” Archiv der Mathematik, Vol. 40, No. 6, 2001, pp. 406-415. doi:10.1007/PL00000451
[3] S. Karadeniz and B. Yildiz, “ (1+v)-Constacyclic Codes over F2+uF2+vF2+uvF2 ,” Journal of the Franklin Institute, Vol. 347, 2011, pp. 2652-2632.
[4] V. Sison and P. Solè, “Bounds on the Minimum Homogeneous Distance of the pT-ary Image of Linear Block Codes over the Galois Ring (pT,m) ,” IEEE transactions on Information Theory, Vol. 53, No. 6, 2007, pp. 2270-2273. doi:10.1109/TIT.2007.896891
[5] X. Xu and X. Liu, “On the Structure of Cyclic Codes over F2+uF2+vF2+uvF2 ,” Wuhan University Journal of Natural Sciences, Vol. 16, No. 5, 2011, pp. 457-460. doi:10.1007/s11859-011-0780-5
[6] B. Yildizand S. Karadeniz, “Linear Codes over F2+uF2+vF2+uvF2 ,” Designs Codes Cryptography, Vol. 54, No. 1, 2010, pp. 61-81. doi:10.1007/s10623-009-9309-8
[7] B. Yildiz and S. Karadeniz, “Self-dual Codes over F2+uF2+vF2+uvF2 ,” Journal of the Franklin Institute, Vol. 347, 2010, No. 10, pp. 1888-1894. doi:10.1016/j.jfranklin.2010.10.007
[8] B. Yildiz and S. Karadeniz, “Cyclic Codes over F2+uF2+vF2+uvF2 ,” Designs Codes Cryptography, Vol. 58, No. 3, 2011, pp. 221-234. doi:10.1007/s10623-010-9399-3

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.