In an earlier paper the authors studied simplex codes of type α and β over 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 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 Z 2 s . The above codes are also shown to satisfy the chain condition.
Lower and upper bounds for R(S k (q)) , the covering radius of a k -dimensional q -ary Simplex codes are determined. These help in getting bounds with a gap of one for S 3 (q) . Exact covering radius of S 2 (q) , S 3 (3) , S 4 (3) , S 4 (4) and S 3 (q) for q even are obtained.
In this paper we determine an upper bound for the covering radius of a q-ary MacDonald code Ù´Õ µ. Values of Ò Õ´ µ, the minimal length of a 4-dimensional q-ary code with minimum distance d is obtained for Õ ¾ ½ and Õ ¾ ¾. These are used to determine the covering radius of ¿ ½´Õ µ, ¿ ¾´Õ µ and ¾´Õ µ.
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