In this work, we study linear locally repairable codes (LRCs) over fixed field size. In the first part, we present new upper bounds on the dimension and minimum distance of linear (r,?)-LRCs with local-error-correcting property. We then give an explicit construction of such codes with optimal minimum distance. In particular, we give several families of d-optimal (r,? =2)-LRCs with d=3 and d=4.
In the second part, we first present new upper bounds on the dimension and minimum distance of linear (r,t)-LRCs with availability. We then study the locality and availability properties of several classes of one-step majority-logic decodable codes, including cyclic Simplex codes, cyclic difference-set codes, and 4-cycle free regular low-density parity-check (LDPC) codes. We also investigate their optimality using the new bounds.
Pengfei Huang received the B.E. degree in Electrical Engineering from Zhejiang University, Hangzhou, China, in 2010 and the M.S. degree in Electrical Engineering from Shanghai Jiao Tong University, Shanghai, China, in 2013. He is currently a Ph.D. student in the ECE department at UCSD and is working in Prof. Siegel’s STAR group. He is interested in wireless communications and storage systems. His current research focuses on distributed storage systems.