Codes for DNA sequence profiles

We consider the problem of storing information on synthetic DNA media and associated coding paradigms. The focal question of our analysis it how to construct and enumerate sequences that may be discriminated based on their collection of substrings observed through two types of noisy sequencing channels. In particular, we consider DNA sequences with balanced GC content, needed for chemical stability and desirable hybridization properties. We show that restricted de Bruijn graphs and Ehrhart theory for rational polytopes provide a suitable framework for studying such combinatorial questions.