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For integer r satisfying 0\leq r\leq p-2, a sequence family \Omega_r of polyphase sequences of prime period p, size (p-2)p^r, and maximum correlation at most 2+(r+1)\sqrtp is presented. The sequence families are nested, that is, \Omega_r is contained in \Omegar+1, which provides design flexibility with respect to family size and maximum correlation. The sequences in \Omega_r are derived from a combination of multiplicative and additive characters of a prime field. Estimates on hybrid character sums are then used to bound the maximum correlation. This construction generalizes \Omega_0, which was previously proposed by Scholtz and Welch. Sequence family \Omega_2 is closely related to a recent design by Wang and Gong, who bounded its maximum correlation using methods from representation theory and asked for a more direct proof of this bound. Such a proof is given here and an improvement of the bound is provided. [ABSTRACT FROM AUTHOR]

For odd integer m ≥ 3 and $${t=0,1,\ldots,\frac{m-1}{2}}$$, we define Family $${\fancyscript{V}(t)}$$ to be a set of size 2 containing binary sequences of period 2 − 2. The nontrivial correlations between sequences in Family $${\fancyscript{V}(t)}$$ are bounded in magnitude by 2 + 2. Families $${\fancyscript{V}(0)}$$ and $${\fancyscript{V}(1)}$$ compare favourably to the small and large Kasami sets, respectively. So far, the correlation distribution of Family $${\fancyscript{V}(t)}$$ is only known for t = 0. A general framework for computing the correlation distribution of Family $${\fancyscript{V}(t)}$$ is established. The correlation distribution of $${\fancyscript{V}(1)}$$ is derived, and a way to obtain the correlation distribution of $${\fancyscript{V}(2)}$$ is described. [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]