Paper 2010/163 Original: eprint.iacr.org/2010/163 ↗

Golay Complementary Sequences Over the QAM Constellation

Abstract

In this paper, we present new constructions for $ M^{2}$ -QAM and $2M$ $Q$-$PAM$ Golay complementary sequences of length $2^n$ for integer $n$, where $M=2^{m}$ for integer $m$. New decision conditions are proposed to judge whether an offset pairs can be used to construct the Golay complementary sequences over constellation, and with the new decision conditions, we prove the conjecture 1 proposed by Ying Li~\cite{16}. We describe a new offset pairs and construct new $64$-$QAM$ Golay sequences based on this new offset pairs. We also study the $128$-$QAM$ Golay complementary sequences, and propose a new decision condition to judge whether the sequences are $128$-$QAM$ Golay complementary.