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The number of zeros and the number of ones in a binary string are referred to as the composition of the string, and the prefix-suffix compositions of a string are a multiset formed by the compositions of the prefixes and suffixes of all possible lengths of the string. In this work, we present binary codes of length n in which every codeword can be efficiently reconstructed from its erroneous prefix-suffix compositions with at most t composition errors.

This paper studies two problems that are motivated by the novel recent approach of composite DNA that takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm, every composite symbols does not store a single nucleotide but a mixture of the four DNA nucleotides. The first problem studies the expected number of strand reads in order to decode a composite strand or a group of composite strands.