Generalized construction of cyclic (<i>r</i>, <i>t</i>)-locally repairable codes using trace function

Abstract

With an increasing demand for distributed systems storing big data, locally repairable codes (LRCs) have attracted attentions to recover lost data on failure nodes. An (r, t)-LRC has the property that each coordinate of codewords can be recovered from at most r other coordinates (repair set), and there are at least t disjoint repair sets for each coordinate, where r and t are called locality and availability, respectively. Wang, Zhang, and Lin recently have proposed a construction method of cyclic (r, t)-LRCs that can have high availability with a guaranteed lower bound on the minimum distance. However, due to the lack of flexibility in code design, it is impossible to modify code parameters while keeping the code performance. This letter presents a generalized construction of cyclic (r, t)-LRCs based on the trace function whose high-degree terms are truncated. It is shown that the proposed construction preserves the symbol-repairing performance and therefore provides better flexibility in code design.