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This paper presents an optimized lexical post-processing designed for handwritten word recognition. The aim of this work is to correct recognition and segmentation errors using lexical information from a lexicon. The presented lexical post-processing is based on two phases: in the first phase a lexicon organization is made to reduce the search space into sub-lexicons during the recognition process. The second phase develops a specific edit distance to identify the handwritten word using a selection of the sub-lexicons. The paper exposes two original strategies of lexicon reduction and a new approach to automatically learn an edit distance specifically adapted to the properties of the on-line handwritten word recognition. Experimental results are reported to compare the two lexicon reduction strategies and first results emphasize the impact of the learning process of the new edit distance.