Quaternary constant-amplitude codes for multicode CDMA
IEEE Transactions on Information Theory
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
Galois rings and pseudo-random sequences
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
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Codes which reduce the peak-to-average power (PAPR) in multicode code-division multiple-access (MC-CDMA) communications systems are systematically studied. The problem of designing such codes is reformulated as a new coding-theoretic problem: codes with low PAPR are ones in which the codewords are far from the first-order Reed-Muller code. Bounds on the tradeoff between rate, PAPR, and error-correcting capability of codes for MC-CDMA follow. The connections between the code design problem, bent functions, and algebraic coding theory (in particular, the Kerdock codes and Delsarte-Goethals codes) are exploited to construct code families with flexible parameters for the small values of n of practical interest. In view of their algebraic structure, these codes enjoy efficient encoding and decoding algorithms. The correspondence concludes by listing open problems in algebraic coding theory and Boolean functions motivated by the correspondence.