In this talk, I will present a connection between designing low
correlation zone (LCZ) sequences and the results of correlation
of sequences with subfield decompositions. This results
in low correlation zone signal sets with huge sizes over three
different alphabetic sets: finite field of size $q$, integer
residue ring modulo $q$, and the subset in the complex field which
consists of powers of a primitive $q$-th root of unity. A connection between these
constructions and ``completely
non-cyclic'' Hadamard matrices will be shown. I will also provide some open problems
along this direction.
Joint work with Solomon W. Golomb and Hongyeop Song.