On Optimal Pseudo-cyclic (r, δ) Locally Repairable Codes

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 F-q, x(n) - a only has quadratic factors over F-q for even n and k. Based on these facts, we consider the constructions of optimal q - ary pseudo-cyclic (r, delta) locally repairable codes (LRCs) with length n vertical bar q + 1 in this paper. To be specific, we obtain four classes of optimal pseudo- cyclic (r, delta)-LRCs with new parameters.