New Construction of $M$-Ary Sequence Families With Low Correlation From the Structure of Sidelnikov Sequences
Nam Yul Yu, Guang Gong · IEEE Transactions on Information Theory · 2010
For primepand a positive integerm, it is shown thatM-ary Sidelnikov sequences of periodp2m-1, ifM|pm-1, can be equivalently generated by the operation of elements in a finite fieldGF(pm), including apm-arym-sequence. From the(pm-1) ×(pm+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 newM-ary sequence families of periodpm-1. In particular, newM-ary sequence families of periodpm-1 are constructed 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 newM-ary sequence family of periodpm-1 and the maximum correlation magnitude2√{pm}+6 asymptotically achieves√2times the equality of the Sidelnikov's lower bound whenM=pm-1 for odd primep.