Using methods from finite field theory, I have developed a new technique for generating sequences with low correlations. The resulting sequence families are competitive with previously designed families in resulting system capacity, but have the added advantage of resistance to certain cryptologic attacks and to jamming. This is an advantage in situations such as mobile phone systems where eavesdropping is a concern. These results appear in d-Form Sequences: Families of Sequences with Low Correlation Values and Large Linear Span which was in the 1993 Allerton Conference Proceedings and will appear in the IEEE Transactions on Information Theory and Large Families of Sequences with Near Optimal Correlations and Large LinearSpans which appeared in 1993 Allerton Conference Proceedings. The techniques developed will likely lead to the construction of other such families of sequences.
Other recent projects involve analyzing statistical properties of partial period correlations of geometric sequences (Partial Period Autocorrelations of Geometric Sequences, with Mark Goresky, IEEE Transactions on Information Theory IT-40 (1994) 494-502, and Partial Period Cross Correlations of Geometric Sequences, to appear in IEEE Transactions on Information Theory) and analyzing cross-correlations of quadratically decimated geometric sequences in both odd and even characteristic (Cross-Correlations of Geometric Sequences in Characteristic Two, Designs, Codes, and Cryptography vol. 3 (1993) 347-377 and Cross-Correlations of Quadratic Form Sequences in Odd Characteristic, to appear in Designs, Codes, and Cryptography).
This material is based upon work supported by the National Science Foundation under Grant No. 9400762.