Spectrally Bounded Sequences, Codes, and States: Graph Constructions and Entanglement
Proceedings of the 8th IMA International Conference on Cryptography and Coding
Golay complementary array pairs
Designs, Codes and Cryptography
A new turbo coding approach to reduce the Peak-to-Average Power Ratio of a multi-antenna-OFDM system
International Journal of Mobile Communications
PAPR reduction via linear phase variations
ICCOM'05 Proceedings of the 9th WSEAS International Conference on Communications
A multi-dimensional approach to the construction and enumeration of Golay complementary sequences
Journal of Combinatorial Theory Series A
A Study on the Pseudorandom Properties of Sequences Generated Via the Additive Order
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Quaternary constant-amplitude codes for multicode CDMA
IEEE Transactions on Information Theory
WCNC'09 Proceedings of the 2009 IEEE conference on Wireless Communications & Networking Conference
Generalized Reed---Muller codes over $${\mathbb{Z}_q}$$
Designs, Codes and Cryptography
Note: A new source of seed pairs for Golay sequences of length 2m
Journal of Combinatorial Theory Series A
Novel sequence design for low-PMEPR and high-code-rate OFDM systems
IEEE Transactions on Communications
Bent functions and codes with low peak-to-average power ratio for multi-code CDMA
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Near-complementary sequences of various lengths and low PMEPR for multicarrier communications
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Construction of M-QAM sequences based on generalized Rudin-Shapiro polynomials
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
PAPR reduction of OFDM using PTS and error-correcting code subblocking
IEEE Transactions on Wireless Communications
A construction of general QAM Golay complementary sequences
IEEE Transactions on Information Theory
A new construction of 16-QAM near complementary sequences
IEEE Transactions on Information Theory
Quaternary Golay sequence pairs I: even length
Designs, Codes and Cryptography
Constructions of complementary sequences for power-controlled OFDM transmission
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Complementary sets and reed-muller codes for peak-to-average power ratio reduction in OFDM
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Wireless Personal Communications: An International Journal
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
A complementary construction using mutually unbiased bases
Cryptography and Communications
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Controlling the peak-to-mean envelope power ratio (PMEPR) of orthogonal frequency-division multiplexed (OFDM) transmissions is a notoriously difficult problem, though one which is of vital importance for the practical application of OFDM in low-cost applications. The utility of Golay complementary sequences in solving this problem has been recognized for some time. In this paper, a powerful theory linking Golay complementary sets of polyphase sequences and Reed-Muller codes is developed. Our main result shows that any second-order coset of a q-ary generalization of the first order Reed-Muller code can be partitioned into Golay complementary sets whose size depends only on a single parameter that is easily computed from a graph associated with the coset. As a first consequence, recent results of Davis and Jedwab (see Electron. Lett., vol.33, p.267-8, 1997) on Golay pairs, as well as earlier constructions of Golay (1949, 1951, 1961), Budisin (1990) and Sivaswamy (1978) are shown to arise as special cases of a unified theory for Golay complementary sets. As a second consequence, the main result directly yields bounds on the PMEPRs of codes formed from selected cosets of the generalized first order Reed-Muller code. These codes enjoy efficient encoding, good error-correcting capability, and tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using small numbers of carriers