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**1 - 3**of**3**### 1New Constructions of General QAM Golay Complementary Sequences

"... There have been five constructions (Case I to Case V) of 64-QAM Golay complementary sequences (GCSs), of which the Case IV and Case V constructions were identified by Chang, Li, and Hirata in 2010. The Generalized Cases I-III constructions for 4q-QAM (q ≥ 1) GCSs were additionally proposed by Li. In ..."

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There have been five constructions (Case I to Case V) of 64-QAM Golay complementary sequences (GCSs), of which the Case IV and Case V constructions were identified by Chang, Li, and Hirata in 2010. The Generalized Cases I-III constructions for 4q-QAM (q ≥ 1) GCSs were additionally proposed by Li. In this paper, the Generalized Case IV and Generalized Case V constructions for 4q-QAM (q> = 3) GCSs are proposed using selected Gaussian integer pairs, each of which contains two distinct Gaussian integers with identical magnitude and which are not conjugate with each other. Index Terms Golay complementary sequence (GCS), QAM, orthogonal frequency-division multiplexing (OFDM), peak-to-mean envelope power ratio (PMEPR), Gaussian integer. I.

### 1New Complete Complementary Codes for Peak-to-Mean Power Control in Multi-Carrier CDMA

"... Owing to the zero non-trivial aperiodic correlation sum properties, complete complementary codes (CCC) have been applied to asynchronous multi-carrier code-division multiple-access (MC-CDMA) communications in order to provide zero interference performance. When each complementary code is arranged to ..."

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Owing to the zero non-trivial aperiodic correlation sum properties, complete complementary codes (CCC) have been applied to asynchronous multi-carrier code-division multiple-access (MC-CDMA) communications in order to provide zero interference performance. When each complementary code is arranged to be a matrix, the peak-to-mean envelope power ratio (PMEPR) of the CCC-MC-CDMA system is determined by the column sequences of the complementary matrices. The existing CCC have the column sequence PMEPR of M, where M denotes the number of subcarriers in a CCC-MC-CDMA system. In practice, M is generally large and a PMEPR approaching this value is unacceptable. To solve this problem, a new class of CCC using generalized Boolean functions and with a column sequence PMEPR of at most 2 is proposed in this paper.

### Optimal Odd-Length Binary Z-Complementary Pairs

, 2013

"... A pair of sequences is called a Golay complementary pair (GCP) if their aperiodic auto-correlation sums are zero for all out-of-phase time shifts. Existing known binary GCPs only have even-lengths in the form of 21026 (where ; ;
are non-negative integers). To fill the gap left by the odd-lengths, ..."

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A pair of sequences is called a Golay complementary pair (GCP) if their aperiodic auto-correlation sums are zero for all out-of-phase time shifts. Existing known binary GCPs only have even-lengths in the form of 21026 (where ; ;
are non-negative integers). To fill the gap left by the odd-lengths, we investigate the optimal odd-length binary pairs which display the closest correlation property to that of GCPs. Our criteria of “closeness ” is that each pair has the maximum possible zero-correlation zone (ZCZ) width and minimum possible out-of-zone aperiodic auto-correlation sums. Such optimal pairs are called optimal odd-length binary Z-complementary pairs (OB-ZCP) in this paper. We show that each optimal OB-ZCP has maximum ZCZ width of (N+1)=2, and minimum out-of-zone aperiodic sum magnitude of 2, where N denotes the sequence length (odd). Systematic constructions of such optimal OP-ZCPs are proposed by insertion and deletion of certain binary GCPs, which settle the 2011 Li-Fan-Tang-Tu open problem positively. The proposed optimal OB-ZCPs may serve as a replacement for GCPs in many engineering applications where odd sequence lengths are preferred. In addition, they give rise to a new family of base-two almost difference families (ADF) which are useful in studying partially balanced incomplete block design (BIBD).