A note on r-extensible prefix codes (Q1114025)

A prefix code P over X is said to be r-extensible if for every uv\(\in P\) and \(x\in X^*\) there exists \(s\in X^*\) such that \(uxv=ts\) for some \(t\in P\). An ideal I of \(X^*\) is said to be cs-prime if \(x^ 2\in I\) implies that \(x\in I\). In this note, a necessary and sufficient condition for an r-extensible prefix code to be finite is given. The class of all r-extensible prefix codes generating cs-prime ideals is constructed.