On synchronized coded systems

Abstract: We introduce a class of codes with overlapping code words, that we call SPO-codes. The SPO-codes are related to the Markov codes that were introduced in: G. Keller, J. Combinatorial Theory 56, (1991),pp.\ 75--83. The process of generating a coded system from a code extends to SPO-codes. We describe a family of intrinsically ergodic synchronized SPO-coded systems that is closed under topological conjugacy. We construct synchronized subshifts with salient structural features by means of SPO-codes. We construct SPO-coded systems that are not semisynchronized.