$f$-Words and Binary Solid Codes
Stavros Konstantinidis and Joshua Young
Given any unbounded and non-decreasing sequence $f$ of positive integers,
we define an infinite set of binary words, called $f$-words, which constitute
an overlap-free language. We investigate some properties of this language
and then use these properties to define new classes of finite and infinite
binary solid codes -- solid codes have the strongest synchronization and
error-delimiting capabilities in the hierarchies of codes. The infinite
class improves on an earlier construction of solid codes in terms of
average word length (or information rate), without sacrificing their
encoding complexity. The infinite class concerns maximal solid codes and
builds on an earlier work on maximal binary solid codes. This work
constitutes another step towards a systematic structural characterization
of binary maximal solid codes.