A 3-WORD CODE WHICH IS NOT PREFIX-SUFFIX COMPOSED

In this paper, we are concerned with finite p-s-composed codes, that i s with codes obtained by composition of finite prefix and suffix codes . We give a method to decompose a finite prefix-suffix composed code i n a minimal number of prefix and suffix codes. Using this method, we e stablish that every prefix-suffix composed n-word code (n greater than or equal to 3) can be expressed as the composition of at most 2n - 3 prefix and suffix codes. We show that for all n, this limit is reached , that is, there exists a ps-composed n-word code that cannot be expre ssed as the composition of less than 2n - 3 prefix and suffix codes. T hen we give an example of a three-word code which is not prefix-suffix composed, refuting a conjecture proposed by Restive et al. in 1989.