Perfect codes in Cartesian products of 2-paths and infinite paths.
Perfect codes in graphs and their Cartesian powers [Abstract of thesis]
Picture codes
We introduce doubly-ranked (DR) monoids in order to study picture codes. We show that a DR-monoid is free iff it is pictorially stable. This allows us to associate with a set C of pictures a picture code B(C) which is the basis of the least DR-monoid including C. A weak version of the defect theorem for pictures is established. A characterization of picture codes through picture series is also given.
Recursively differentiable quasigroups and complete recursive codes
Criteria of recursive differentiability of quasigroups are given. Complete recursive codes which attains the Joshibound are constructed using recursively differentiable -ary quasigroups.
The structure of generalized quasi cyclic codes.
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.