On the correlation distribution of the Coulter-Matthews decimation

The distribution of the cross correlation between the ternary m-sequence {s_t} of period n=3^m-1 and the decimated sequences {s_dt} and {s_dt+1} of period (3^m-1)/2, where d=3^k+1/2 with k odd and gcd(k,m)=1 is determined. The method to find this distribution is related to the result by Coulter and Matthews that f(x)=x^d is a planar function over GF(3^m).