On Optimal Pseudo-cyclic ($r, \delta$) Locally Repairable Codes
Bin Chen, Shu‐Tao Xia, Jie Hao, Fang‐Wei Fu · 2018
Pseudo-cyclic codes is a generalization of cyclic codes and provides a way to obtain MDS codes with more parameters in coding theory. Specially, if a is not a quadratic residue in Fq, xn-a only has quadratic factors over Fqfor even n and k. Based on these facts, we consider the constructions of optimal q-ary pseudo-cyclic (r, δ) locally repairable codes (LRCs) with length n | q+1 in this paper. To be specific, we obtain four classes of optimal pseudo-cyclic (r, δ) -LRCs with new parameters.