Optimal linear and cyclic locally repairable codes over small fields

Alexander Zeh, Eitan Yaakobi
2015 2015 IEEE Information Theory Workshop (ITW)  
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields with locality properties are developed. The first two approaches give binary cyclic codes with locality two. While the first construction has availability one, the second binary code is characterized by multiple available repair sets based on a binary Simplex
more » ... code. The third approach extends the first one to q-ary cyclic codes including (binary) extension fields, where the locality property is determined by the properties of a shortened first-order Reed-Muller code. Non-cyclic optimal binary linear codes with locality greater than two are obtained by the fourth construction.
doi:10.1109/itw.2015.7133123 dblp:conf/itw/ZehY15 fatcat:r2un6f46n5bgngyvyi6prmjfam