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 (θrms), is approximately equal to the quantity ; L being the period of the sequences. However, θmax, 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.
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Received: January 18, 1999; revised version: October 20, 1999
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Udaya, P., Siddiqi, M. Generalized GMW Quadriphase Sequences Satisfying the Welch Bound with Equality. AAECC 10, 203–225 (2000). https://doi.org/10.1007/s002000050125
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DOI: https://doi.org/10.1007/s002000050125