A recent study by one of the authors has demonstrated the importance of
profile vectors in DNA-based data storage. We provide exact values and lower
bounds on the number of profile vectors for finite values of alphabet size q,
read length â„“, and word length n.Consequently, we demonstrate that for
q≥2 and n≤qℓ/2−1, the number of profile vectors is at least
qκn with κ very close to one.In addition to enumeration
results, we provide a set of efficient encoding and decoding algorithms for
each of two particular families of profile vectors