On the structure of M-ary Sidelnikov sequences of period p2m − 1
Nam Yul Yu, Guang Gong · 2010
For prime p and a positive integer m, it is shown that M-ary Sidelnikov sequences of period p2m- 1, if M | pm- 1, can be equivalently generated by the operation of elements in a finite field GF(pm), including a pm-ary m-sequence. The equivalent representation over GF(pm) requires low complexity for implementing the Sidelnikov sequences. Moreover, a (pm- 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 pm- 1 and their constant multiples have the low correlation magnitude bounded by 3√(pm+ 1).