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We consider the merit factor of binary sequences obtained by appending an initial fraction of an m-sequence to itself. We show that, for all sufficiently large n, there is some rotation of each m-sequence of length n that has merit factor greater than 3.34 under suitable appending. This is the first proof that the asymptotic merit factor of a binary sequence family can be increased under appending. We also conjecture, based on numerical evidence, that each rotation of an m-sequence has asymptotic merit factor greater than 3.34 under suitable appending. Our results indicate that the effect of appending on the merit factor is strikingly similar for m-sequences as for rotated Legendre sequences. [ABSTRACT FROM AUTHOR]

Boolean functions which are simultaneously bent and negabent are studied. Transformations that leave the bent-negabent property invariant are presented. A construction for infinitely many bent-negabent Boolean functions in 2mn variables (m > 1) and of algebraic degree at most n is described, this being a subclass of the Maiorana–McFarland class of bent functions. Finally it is shown that a bent-negabent function in 2n variables from the Maiorona–McFarland class has algebraic degree at most n − 1. [ABSTRACT FROM AUTHOR]

We present constructions of polyphase sequences suitable for the use as codewords in orthogonal frequency-division multiplexing (OFDM) with strictly bounded peak-to-mean envelope power ratio (PMEPR). Our first construction establishes that each polyphase sequence of length 2m lies in a complementary set, whose size depends on a special property of its associated generalized Boolean function. Thus we identify a large family of sequences with PMEPR at most 2k + 1, where k is a non-negative integer. Our second construction yields sequences that lie in so-called almost complementary pairs and have PMEPR at most 3. A number of coding schemes for OFDM with low PMEPR is then presented. These schemes extend and complement previously proposed coding options. [ABSTRACT FROM AUTHOR]