New construction of M -ary sequence families with low correlation from the structure of Sidelnikov sequences

Authors:
Nam Yul Yu;Guang Gong
Affiliations:
Department of Electrical Engineering, Lakehead University, Thunder Bay, ON, Canada;Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

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. 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 new M -ary sequence families of period pm - 1. In particular, new M -ary sequence families of period pm - 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 new M -ary sequence family of period pm - 1 and the maximum correlation magnitude 2√pm + 6 asymptotically achieves √2 times the equality of the Sidelnikov's lower bound when M = pm - 1 for odd prime p.