On the structure of M-ary Sidelnikov sequences of period p2m − 1

For prime p and a positive integer m, it is shown that M-ary Sidelnikov sequences of period p^2m - 1, if M | p^m - 1, can be equivalently generated by the operation of elements in a finite field GF(p^m), including a p^m-ary m-sequence. The equivalent representation over GF(p^m) requires low complexity for implementing the Sidelnikov sequences. Moreover, a (p^m - 1)×(pm+1) array structure is introduced for the Sidelnikov sequences. From the array structure, it is found that about a half of the column sequences of length p^m - 1 and their constant multiples have the low correlation magnitude bounded by 3√(p^m + 1).