Reconstructing words from a fixed palindromic length sequence

To every word w is associated a sequence Gw built by computing at each position i the length of its longest palindromic suffix. This sequence is then used to compute the palindromic defect of a finite word w defined by D(w) = |w| + 1 − |Pal(w)| where Pal(w) is the set of its palindromic factors. In this paper we exhibit some properties of this sequence and introduce the problem of reconstructing a word from Gw. In particular we show that up to a relabelling the solution is unique for 2-letter alphabets.