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)} ofperiod (3(m) - 1)/2, where d = (2)/(3k+1) 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)).
m-sequences planar functions cross-correlation function