報告題目1：A survey on list decoding of classical block codes
报 告 人：邢朝平 教授
報告題目2：Construction of MDS codes with complementary duals
报 告 人：金玲飞 副教授
報告摘要1：In computer science, particularly in coding theory, list decoding is an alternative to unique decoding of error-correcting codes for large error rates. The notion was proposed by Elias in the 1950s. The main idea behind list decoding is that the decoding algorithm instead of outputting a single possible message outputs a list of possibilities one of which is correct. This allows for handling a greater number of errors than that allowed by unique decoding.
The unique decoding model in coding theory, which is constrained to output a single valid codeword from the received word could not tolerate greater fraction of errors. This resulted in a gap between the error-correction performance for stochastic noise models (proposed by Shannon) and the adversarial noise model (considered by Richard Hamming). Since the mid 90s, significant algorithmic progress by the coding theory community has bridged this gap. Much of this progress is based on a relaxed error-correction model called list decoding, wherein the decoder outputs a list of codewords for worst-case pathological error patterns where the actual transmitted codeword is included in the output list. In case of typical error patterns though, the decoder outputs a unique single codeword, given a received word, which is almost always the case (However, this is not known to be true for all codes). The improvement here is significant in that the error-correction performance doubles. This is because now the decoder is not confined by the half-the-minimum distance barrier. This model is very appealing because having a list of codewords is certainly better than just giving up. The notion of list-decoding has many interesting applications in complexity theory.
In this talk, we will survey some known results on list decoding of classical block codes under the adversarial noise model.
報告摘要2：A Linear Complementary Dual (LCD for short) code is a linear code with complimentary dual. LCD codes have been extensively studied in literature. On the other hand, MDS codes are an important class of linear codes that have found wide applications in both theory and practice. This talk is going to show constructions of several classes of MDS codes with complimentary duals (i.e., LCD MDS codes) through generalized Reed-Solomon codes.