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How Long Can Optimal Locally Repairable Codes Bel

Chaoping Xing School of Physical and Mathematical Sciences, Nanyang Technological University , Singapore. https://orcid.org/0000-0002-1257-1033 2 Computer Science Department, Carnegie Mellon University

How Long Can Optimal Locally Repairable Codes Bel

A locally repairable code (LRC) with locality r allows for the recovery of any erased codeword symbol using only r other codeword symbols. A Singleton-type bound dictates the best possible trade-off between the dimension and distance of LRCs - an LRC attaining this trade-off is deemed optimal. Such optimal LRCs have been constructed over alphabets growing linearly in the block...

Lossless Dimension Expanders via Linearized Polynomials and Subspace Designs

.4230/LIPIcs.APPROX-RANDOM. 2014 . 748 . Venkatesan Guruswami , Carol Wang , and Chaoping Xing . Explicit list-decodable rankmetric and subspace codes via subspace designs . IEEE Transactions on ... Information Theory , 62 ( 5 ): 2707 - 2718 , 2016 . Venkatesan Guruswami and Chaoping Xing . Folded codes from function field towers and improved optimal rate list decoding . In Howard J. Karloff and Toniann

Subspace Designs Based on Algebraic Function Fields

. doi:10 .1109/TIT. 2013 . 2246813 . Venkatesan Guruswami , Carol Wang , and Chaoping Xing . Explicit list-decodable rankmetric and subspace codes via subspace designs . IEEE Trans. Information Theory ... , 62 ( 5 ): 2707 - 2718 , 2016 . Preliminary versions in STOC 2013 and RANDOM 2014 . doi: 10 .1109/TIT. 2016 . 2544347 . Venkatesan Guruswami and Chaoping Xing . Folded codes from function fields and