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A binary sequence of length n is an n-tuple with elements in \-1,1\ and its peak sidelobe level is the largest absolute value of its aperiodic autocorrelations at nonzero shifts. A classical problem is to find binary sequences whose peak sidelobe level is small compared to the length of the sequence. Using known techniques from probabilistic combinatorics, this paper gives a construction for a binary sequence of length n with peak sidelobe level at most \sqrt2n\log (2n) for every n > 1. This improves the best known bound for the peak sidelobe level of a family of explicitly constructed binary sequences, which arises for the family of m-sequences. By numerical analysis, it is argued that the peak sidelobe level of the constructed sequences grows in fact like order \sqrtn\log\log n and, therefore, grows strictly more slowly than the peak sidelobe level of a typical binary sequence. [ABSTRACT FROM AUTHOR]

A constant-amplitude code is a code that reduces the peak-to-average power ratio (PAPR) in multicode code-division multiple access (MC-CDMA) systems to the favorable value 1. In this paper, quaternary constant-amplitude codes (codes over Z4) of length 2m with error-correction capabilities are studied. These codes exist for every positive integer m, while binary constant-amplitude codes cannot exist if m is odd. Every word of such a code corresponds to a function from the binary m-tuples to Z4 having the bent property, i.e., its Fourier transform has magnitudes 2m/2. Several constructions of such functions are presented, which are exploited in connection with algebraic codes over Z4 (in particular quaternary Reed-Muller, Kerdock, and Delsarte-Goethals codes) to construct families of quaternary constant-amplitude codes. Mappings from binary to quaternary constant-amplitude codes are presented as well. [ABSTRACT FROM AUTHOR]

The use of error-correcting codes for tight control of the peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency-division multiplexing (OFDM) transmission is considered in this correspondence. By generalizing a result by Paterson, it is shown that each q-phase (q is even) sequence of length 2m lies in a complementary set of size 2k+1, where k is a nonnegative integer that can be easily determined from the generalized Boolean function associated with the sequence. For small k this result provides a reasonably tight bound for the PMEPR of q-phase sequences of length 2m. A new 2 h-ary generalization of the classical Reed-Muller code is then used together with the result on complementary sets to derive flexible OFDM coding schemes with low PMEPR. These codes include the codes developed by Davis and Jedwab as a special case. In certain situations the codes in the present correspondence are similar to Paterson's code constructions and often outperform them. [ABSTRACT FROM AUTHOR]