Clustering-Correcting Codes

Clustering for Designing Error Correcting Codes

Acknowledgements I had the great pleasure of working with Dr. Anamitra Makur during my stay at the Institute. But for him, this thesis would not have seen light. I would like to thank him for the help he has rendered during this work. Suryan for their help. Jyothish and Jemlin for making my stay at the Institute a happy and memorable one. P r a h h and Mala who had been always helpful to me. Fi...

One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

Codes Correcting Two Deletions

In this work, we investigate the problem of constructing codes capable of correcting two deletions. In particular, we construct a code that requires redundancy approximately 8 log2 n+O(log2 log2 n) bits of redundancy, where n denotes the length of the code. To the best of the author’s knowledge, this represents the best known construction in that it requires the lowest number of redundant bits ...

Synchronizable Error-Correcting Codes

A new technique for correcting synchronization errors in the transmission of discrete-symbol information is developed. The technique can be applied to any t-additive-error-correcting Bose-Chaudhuri-Hocquenghem code, to provide protection against synchronization errors. The synchronization error is corrected at the first complete received word after the word containing the synchronization error,...

Parallel error correcting codes