In this paper, we investigate the Hamming correlation properties of column sequences from the (q-1)×qd-1q-1 array structure of M-ary Sidelnikov sequences of period qd- 1 for M| q- 1 and d≥ 2. We prove that the proposed set Γ(d) of some column sequences has the maximum non-trivial Hamming correlation upper bounded by the minimum of q-1Md-1 and M-1M[(2d-1)q+1]+q-1M. When M= q- 1 , we show that Γ(d) is optimal with respect to the Singleton bound. The set Γ(d) can be extended to a much larger set Δ(d) by involving all the constant additions of the members of Γ(d) , which is also optimal with respect to the Singleton bound when M= q- 1.
Bibliographical noteFunding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1A2B4011191).
All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Applied Mathematics