A note on low-correlation zone signal sets

In this correspondence, we present a connection between designing low-correlation zone (LCZ) sequences and the results of correlation of sequences with subfield decompositions presented in a recent book by the first two authors. This results in LCZ 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. We show a connection between these sequence designs and "completely noncyclic" Hadamard matrices and a construction for those sequences. We also provide some open problems along this direction. Index Terms--Hadamard matrices of completely noncyclic type, low-correlation zone (LCZ) sequences, subfield reducible sequences, two-tuple balance property.