The correlation values and the distribution of these correlation values for the small set of nonbinary Kasami sequences over GF(p) (p prime) are presented. The correlation results are an extension of the binary results and have p+2 correlation levels. This nonbinary Kasami set is asymptotically optimum with respect to its correlation properties. These sequences are obtained, as in the binary case, from a large primitive polynomial of degree n=2 m and a small primitive polynomial of degree m that yields a sequence length of p/sup n/-1 and maximum nontrivial correlation value of 1+p/sup m/. Nonbinary Kasami sequences are directly implemented using shift registers and are applicable for code division multiple access systems.>

Normally, frequency hopping sequences for spread-spectrum communication systems are obtained by selecting groups of elements of binary m sequences. An alternative to using groups of binary m-sequence elements is developed. It involves obtaining nonbinary m sequences with the number of desired hopping frequencies equal to the number of symbols in the finite field which the nonbinary m sequence is over. The grouping of elements of binary m sequences does not necessarily have the m sequences. In addition, the autocorrelation function of the nonbinary m sequence has a maximal period, whereas the frequency hopping sequences obtained from the grouping of elements of binary m sequences may not have a maximal period.>