New Construction of -Ary Sequence Families With Low Correlation From the Structure of Sidelnikov Sequences

摘要

For prime $p$ and a positive integer $m$ , it is shown that $M$-ary Sidelnikov sequences of period $p^{2m}-1$, if $M mid p^m-1$, can be equivalently generated by the operation of elements in a finite field ${rm GF}(p^m)$, including a $p^m$-ary $m$ -sequence. From the $(p^m-1) times (p^m+1)$ array structure of the sequences, it is then found that a half of the column sequences and their constant multiples have low correlation enough to construct new $M$ -ary sequence families of period $p^m-1$. In particular, new $M$-ary sequence families of period $p^m-1$ are constructed-n-n from the combination of the column sequence families and known Sidelnikov-based sequence families, where the new families have larger family sizes than the known ones with the same maximum correlation magnitudes. Finally, it is shown that the new $M$ -ary sequence family of period $p^m-1$ and the maximum correlation magnitude $2sqrt{p^m}+6$ asymptotically achieves $sqrt{2}$ times the equality of the Sidelnikov's lower bound when $M=p^m-1$ for odd prime $p$.