Frequency hopping sequences with optimal partial autocorrelation properties

We classify some p^k-ary (p prime, k integer) generalized m-sequences and generalized Gordon-Mills-Welch (GMW) sequences of period p^2k - 1 over a residue class ring R = GF (p [ξ⌉/(ξ^k) having optimal partial Hamming autocorrelation properties. In frequency hopping (FH) spread-spectrum systems, these sequences are useful for synchronizing process. Suppose, for example, that a transmitting p^k-ary FH patterns of period p^2k - 1 are correlated at a receiver. Usually, the length of a correlation window, denoted by L, is shorter than the pattern's overall period. In that case, the maximum value of the out-of-phase Hamming autocorrelation is lower-bounded by ⌈^L/p^k + 1⌉ but the classified sequences achieve this bound with equality for any positive integer L.