2006/04/18 by Constanza Riera, Riera, Constanza, Lars Eirik Danielsen +3 · 2 citations
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Error Correcting Code Techniques #FOS: Mathematics #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.math/0604396
1 figure, 20 pages
arxiv created 2006/04/18 · openalex publication_date 2006/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive a spectral interpretation of the pivot operation on a graph and generalise this operation to hypergraphs. We establish lower bounds on the number of flat spectra of a Boolean function, depending on internal structures, with respect to the I,Hn and I,H,Nn sets of transforms. We also construct a family of Boolean functions of degree higher than two with a large number of flat spectra with respect to I,Hn, and compute a lower bound on this number. The relationship between pivot orbits and equivalence classes of error-correcting codes is then highlighted. Finally, an enumeration of pivot orbits of various types of graphs is given, and it is shown that the same technique can be used to classify codes.