In Rains has shown that for any linear code C over ZZ_4, d_H, the minimum Hammimg distance of C and d_L, the minimum Lee distance of C satisfy d_H.=>[d_L/2] C is said to be of type α(β)if d_H =[d_L/2] (d_H > [d_L/2]. In this paper we define Simplex codes of type αand ? namely, )S_k~αand S_k~β, respectively over ZZ_4. Some fundamental properties like 2-dimension, Hamming and Lee weight distributions, weight hierarchy etc. are determined for these codes. It is shown that binary images of S_k~αand S_k~βby the Gray map give rise to some interesting binary codes.
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