On Codes with Low Peak-to-Average Power Ratio for Multi-Code CDMA

Codes which reduce the peak-to-average power (PAPR) in multi-code 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 rst-order ReedMuller code. Bounds on the trade-o 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 exible parameters for the small values of n of practical interest. In view of their algebraic structure, these codes enjoy e cient encoding and decoding algorithms. The paper concludes by listing open problems in algebraic coding theory and Boolean functions motivated by the paper.