Reconstruction of Strings From Their Substrings Spectrum

This paper studies reconstruction of strings based upon their substrings spectrum. Under this paradigm, it is assumed that all some fixed length are received and the goal to reconstruct string. While many existing works error free, we follow in noisy setup problem was first studied by Gabrys Milenkovic. The study twofold. First which not multispectrum received, then focus on case where read free. In each provide specific code constructions guaranteed even presence failure either model. We present efficient encoding decoding maps analyze cardinality constructions, while studying cases rates our codes approach 1.