This dissertation is concerned with algebraic list- decoding of error-correcting codes. During the past decade, significant advances in this are were achieved. The breakthrough papers of Sudan, Guruswami & Sudan, and Koetter & Vardy showed that the well-known Reed-Solomon (and other algebraic) codes can correct many more errors - - in the list-decoding sense -- than previously thought possible. Herein, we extend the theory developed in these seminal papers, and improve upon the results reported therein. We first extend the bivariate polynomial interpolation method of Guruswami-Sudan to multivariate interpolation decoding. To this end, we develop a new decoding algorithm for Reed-Solomon codes, which decodes some M codewords together. We show that if the channel errors are synchronized then, with high probability, our multivariate interpolation decoding algorithm corrects up to
نام شخص به منزله سر شناسه - (مسئولیت معنوی درجه اول )