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.