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.
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. 1, 2013, pp. 27-31. doi: 10.4236/ojapps.2013.31B1006.
 S. T. Dougherty, M. K. Gupta and K. Shiromoto, “On Generalized Weights for Codes over Finite Rings,” pre-print, 2002.
 T. Honold, “A Characterization of Finite Frobenius Rings,” Archiv der Mathematik, Vol. 40, No. 6, 2001, pp. 406-415. doi：10.1007/PL00000451
 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.
 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
 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.
 B. Yildizand S. Karadeniz, “Linear Codes over F2+uF2+vF2+uvF2 ,” Designs Codes Cryptography, Vol. 54, No. 1, 2010, pp. 61-81.
 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.
 B. Yildiz and S. Karadeniz, “Cyclic Codes over F2+uF2+vF2+uvF2 ,” Designs Codes Cryptography, Vol. 58, No. 3, 2011, pp. 221-234.