In an earlier paper the authors studied simplex codes of type α and β over ${\mathbb{Z}}_4$ and o... more In an earlier paper the authors studied simplex codes of type α and β over ${\mathbb{Z}}_4$ 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 ${\mathbb{Z}}_{{2^s}}.$ 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 ${\mathbb{Z}}_{2^{s}}.$ The above codes are also shown to satisfy the chain condition.
In an earlier paper the authors studied simplex codes of type α and β over ${\mathbb{Z}}_4$ and o... more In an earlier paper the authors studied simplex codes of type α and β over ${\mathbb{Z}}_4$ 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 ${\mathbb{Z}}_{{2^s}}.$ 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 ${\mathbb{Z}}_{2^{s}}.$ The above codes are also shown to satisfy the chain condition.
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Papers by Manish Gupta