Optimal Large Linear Complexity Frequency Hopping Patterns Derived from Polynomial Residue Class Rings

We construct new sequences over finite rings having optimal Hamming correlation properties. These sequences are useful in frequency hopping multiple-access (FHMA) spread-spectrum communication systems. Our constructions can be classified into linear and nonlinear categories, both giving optimal Hamming correlations according to Lempel-Greenberger (1974) bound. The nonlinear sequences have large linear complexity and can be seen as a generalized version of GMW sequences over fields.

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