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 qth 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.
Bibliographical noteFunding Information:
Manuscript received February 25, 2006; revised September 14, 2006. The work of H.-Y. Song was supported by the Basic Research Program of the Korea Science & Engineering Foundation under Grant (R01-2003-000-10330-0). The material in this correspondence was presented in part at the 2006 Conference of Information Sciences and Systems, Princeton University, Princeton, NJ, March 2006.
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Science Applications
- Library and Information Sciences