(1) Department of Electrical and Computer Engineering, Ohio State University, Columbus, OH 43210, USA;(2) Department of Mathematics, Indian Institute of Technology, Kanpur, India
Abstract:
In an earlier paper the authors studied simplex codes of type α and β over
and obtained some known binary linear and nonlinear codes as Gray images of these codes. In this correspondence, we study weight distributions of simplex codes of type α and β over
The generalized Gray map is then used to construct binary codes. The linear codes meet the Griesmer bound and a few non-linear codes are obtained that meet the Plotkin/Johnson bound. We also give the weight hierarchies of the first order Reed-Muller codes over
The above codes are also shown to satisfy the chain condition.A part of this paper is contained in his Ph.D. Thesis from IIT Kanpur, India