Optimal LRC codes for all lenghts n <= q
Oleg Kolosov, Alexander Barg, Itzhak Tamo, and Gala Yadgar
TL;DR
This paper extends the construction of distance-optimal locally repairable codes (LRCs) from Reed-Solomon subcodes to all lengths n <= q, removing the previous restriction that n must be a multiple of r+1.
Contribution
It introduces a method to shorten existing LRC codes to achieve distance optimality for any length n <= q, broadening their applicability.
Findings
Distance-optimal LRCs for all lengths n <= q
Method to shorten codes while maintaining optimality
Codes applicable beyond previous length restrictions
Abstract
A family of distance-optimal LRC codes from certain subcodes of -ary Reed-Solomon codes, proposed by I.~Tamo and A.~Barg in 2014, assumes that the code length is a multiple of By shortening codes from this family, we show that it is possible to lift this assumption, still obtaining distance-optimal codes.
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Taxonomy
TopicsCoding theory and cryptography · Cellular Automata and Applications · graph theory and CDMA systems