A Note on Low-Correlation Zone Signal Sets

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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 <emphasis><formula formulatype="inline"><tex>$q$</tex></formula></emphasis>, integer residue ring modulo <emphasis><formula formulatype="inline"><tex>$q$</tex> </formula></emphasis>, and the subset in the complex field which consists of powers of a primitive <emphasis><formula formulatype="inline"><tex>$q$</tex> </formula></emphasis>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. </para>