|| On Optimal Quaternary Locally Repairable Codes
||Jie Hao, Beijing University of Posts and Telecommunications, China; Kenneth W. Shum, The Chinese University of Hong Kong (Shenzhen), China; Shu-Tao Xia, Tsinghua University, China; Fang-Wei Fu, Nankai University, China; Yixian Yang, Beijing University of Posts and Telecommunications, China|
||D7-S5-T4: Locally Recoverable Codes I
||Tuesday, 20 July, 23:20 - 23:40
||Tuesday, 20 July, 23:40 - 00:00
A q-ary (n,k,r) locally repairable code (LRC) is an [n,k,d] linear code where every code symbol can be repaired by accessing at most r other code symbols. Its minimum distance satisfies the well-known Singleton-like bound. In this paper, we determine all the possible parameters of quaternary LRCs attaining this Singleton-like bound by employing a parity-check matrix approach. Explicit optimal code constructions are given for all the possible parameters.