Über die minimale Fixpunktanzahl von Dickson-Permutationen auf Galoisfeldern.
Uniformly bounded duplication codes
Duplication is the replacement of a factor w within a word by ww. This operation can be used iteratively to generate languages starting from words or sets of words. By undoing duplications, one can eventually reach a square-free word, the original word's duplication root. The duplication root is unique, if the length of duplications is fixed. Based on these unique roots we define the concept of duplication code. Elementary properties are stated, then the conditions under which infinite duplication...
Uniqueness of the spherical code.
Universal codes and unimodular lattices
Binary quadratic residue codes of length produce via construction and density doubling type II lattices like the Leech. Recently, quaternary quadratic residue codes have been shown to produce the same lattices by construction modulo . We prove in a direct way the equivalence of these two constructions for . In dimension 32, we obtain an extremal lattice of type II not isometric to the Barnes-Wall lattice . The equivalence between construction modulo plus density doubling and construction...