Explicit Constructions of Two-Dimensional Reed-Solomon Codes in High Insertion and Deletion Noise Regime
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Insertion and deletion (insdel for short) errors are synchronization errors in communication systems caused by the loss of positional information in the message. On top of its wide interest in its error correcting capability in the classical setting, Reed-Solomon codes also prove to have error correcting algorithms under insdel metric which is based on Guruswami-Sudan decoding algorithm. Despite this, there have been few studies on the insdel correcting capability of Reed-Solomon codes. Our contributions mainly consist of two parts. Firstly, we construct a family of 2-dimensional Reed-Solomon codes with insdel error correcting capability up to half its length. This result improves the insdel error correcting capability from the previous existing construction which was only logarithmic on the code length. Then, we provide an extension to the first construction to have insdel error correcting capability up to its length. In consequence, the asymptotic minimum insdel distance of our family achieves the upper bound provided by the Singleton bound. Furthermore, it provides an explicit family of Reed-Solomon codes which can be decodable against insdel errors up to its length.
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