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.