This paper will investigate the properties of cyclic codes under the transformation,$ It is discovered that for all the non-shortened cyclic codes (binary or (/-nary), if (g(x), (x−1)) =1 then the set of all the codewords is invariant under the transformation fb. If (g(x), Lx−1)) = (x; − 1), then the set of all the code words is generated by g(x)/(x − 1). Next this paper shows a systematic method for the construction of orthogonal cyclic codes in which all the code vectors are orthogonal to each other even to itself