Rudin-Shapiro sequences on compact groups

Generalized Rudin – Shapiro sequences

Generalised Rudin-Shapiro Constructions

A Golay Complementary Sequence (CS) has Peak-to-Average-Power-Ratio (PAPR) ≤ 2.0 for its one-dimensional continuous Discrete Fourier Transform (DFT) spectrum. Davis and Jedwab showed that all known length 2m CS, (GDJ CS), originate from certain quadratic cosets of Reed-Muller (1,m). These can be generated using the Rudin-Shapiro construction. This paper shows that GDJ CS have PAPR ≤ 2.0 under a...

Gowers norms for the Thue-Morse and Rudin-Shapiro sequences

We estimate Gowers uniformity norms for some classical automatic sequences, such as the Thue-Morse and Rudin-Shapiro sequences. The methods are quite robust and can be extended to a broader class of sequences. As an application, we asymptotically count arithmetic progressions of a given length in the set of integers ≤ N where the Thue-Morse (resp. RudinShapiro) sequence takes the value +1.

Golay-Davis-Jedwab Complementary Sequences and Rudin-Shapiro Constructions

A Golay Complementary Sequence (CS) has a Peak-to-AveragePower-Ratio (PAPR) ≤ 2.0 for its one-dimensional continuous Discrete Fourier Transform (DFT) spectrum. Davis and Jedwab showed that all known length 2 CS, (GDJ CS), originate from certain quadratic cosets of Reed-Muller (1,m). These can be generated using the RudinShapiro construction. This paper shows that GDJ CS have a PAPR ≤ 2.0 under ...

On Sums of Rudin-shapiro Coefficients Ii

Let {a(n)} be the Rudin-Shapiro sequence, and let s(n) = Σ£=o () and t(n) = I"k=0(-\) a(k). In this paper we show that the sequences {s{n)/ Jn) and {t{n)/ Jn) do not have cumulative distribution functions, but do have logarithmic distribution functions (given by a specific Lebesgue integral) at each point of the respective intervals [γ/3/5, yfβ] and [0, V^] The functions a(x) and s(x) sore also...