Technical Program

Paper Detail

Paper IDM.3.3
Paper Title Weight Distributions of q-ary Optimal Locally Repairable Codes with Locality 2, Distance 5 and Even Dimension
Authors Jie Hao, Beijing University of Posts and Telecommunications, China; Jun Zhang, Capital Normal University, China; Shu-Tao Xia, Tsinghua University, China; Fang-Wei Fu, Nankai University, China; Yi-Xian Yang, Beijing University of Posts and Telecommunications, China
Session M.3: Codes for Distributed Storage III
Presentation Lecture
Track Coding for Storage and Memories
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract The weight distribution of a q-ary [n,k,d] linear code is an important research subject in coding theory. In a linear code, a code symbol is said to have locality r if it can be recovered by accessing at most r other code symbols. A q-ary locally repairable code (LRC) is an [n,k,d] linear code over F_q such that every code symbol has locality r, and is said to be optimal if the minimum distance attains the well-known Singleton-like bound. In this paper, we focus on the weight distributions of q-ary optimal LRCs with locality 2, minimum distance 5 and even dimension k. By analyzing the parity-check matrices involving locality, it is shown that the weight distributions of all q-ary optimal LRCs with locality 2, distance 5, even dimension k and code length n can be uniquely determined and explicit expressions of the weight distributions are given.

Plan Ahead


2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

Visit Website!