Generalized GMW Quadriphase Sequences Satisfying the Welch Bound with Equality

Abstract.

This paper gives new families of quadriphase sequences obtained from large linear complexity sequences over Z ₄ by making use of generalized permutation monomials over Galois rings. The construction of these sequences can be seen as a generalization of the binary GMW sequence construction and hence they are referred to as GGMW sequences over Z ₄. The GGMW families satisfy the Welch bound on inner products with equality and it is shown that the root mean square of all the crosscorrelations and out-of-phase autocorrelations (θ_rms), is approximately equal to the quantity ; L being the period of the sequences. However, θ_max, the maximum magnitude of periodic crosscorrelation and out-of-phase autocorrelation, deviates from the optimal value of . Computer results suggest that the number of crosscorrelation values which deviate from the optimal value of is small. The weight structure of these sequences is the same as those of m-sequences over Z ₄. The linear complexity (LC) of the sequences is computed using a generalized Blahuts theorem on the LC of sequences over Z ₄.