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

has been cited by the following article:

• TITLE: Images of Linear Block Codes over Fq+uFq+vFq+uvFq

  AUTHORS: Jane D. Palacio, Virgilio P. Sison

  KEYWORDS: q-ary Images; Distance Bounds

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.3 No.1B1, July 11, 2013

  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.