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cs.IT2022
Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery
Nicolas Resch, Chen Yuan, Yihan Zhang
In this work we consider the list-decodability and list-recoverability of arbitrary -ary codes, for all integer values of . A code is called -list-decodable if…
cs.IT2022
Upper bounds on maximum lengths of Singleton-optimal locally repairable codes
Shu Liu, Tingyi Wu, Chaoping Xing +1
A locally repairable code is called Singleton-optimal if it achieves the Singleton-type bound. Such codes are of great theoretic interest in the study of locally repairable codes.…
cs.IT2022
Threshold Rates of Codes Ensembles: Linear is Best
Nicolas Resch, Chen Yuan
In this work, we prove new results concerning the combinatorial properties of random linear codes. Firstly, we prove a lower bound on the list-size required for random linear codes…