Cyclic operators for columns of the matrices of discrete transforms
The author considers cyclic permutations of the columns of a matrix and their application to Hadamard-Sylvester matrices of order \(2^n\). Investigated are recursive algorithms for the construction of such permutations of discrete Walsh transforms in both the Hadamard and the Paley enumerations, along with results on eigenspaces and connection to the Fourier transform of the auxiliary matrices appearing in these algorithms. For the background of this work, see, e.g., the author's paper [Probl. Inf. Transm. 46, No. 3, 253--271 (2010); translation from Probl. Peredachi Inf. 46, No. 3, 60--79 (2010; Zbl 1241.94018)] and the book by Schipp, Wade, and Simon [\textit{F. Schipp} et al., Walsh series. An introduction to dyadic harmonic analysis. With the assistance from J. Pál. Bristol etc.: Adam Hilger (1990; Zbl 0727.42017)].
scientific article; zbMATH DE number 6497499