$f$-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.