MDS Symbol-Pair Cyclic Codes of Length 2p^s over \mathbb F

Let p be an odd prime, s and m be positive integers. Cyclic codes of length 2p^{{s}} over \mathbb {F}_{{p}^{{m}}} are the ideals \langle ( {x}-1)^{i}({x}+1)^{j} \rangle , where 0 \le {i}, {j} \le {p}^{ {s}} , of the principal ideal ring \mathbb {F}_{{p}^{{m}}}[{x}]/\langle {x}^{2\textit {p}^{\textit {s}}}-1 \rangle . Using this structure, the symbol-pair distances of all cyclic codes of length 2\textit {p}^{\textit {s}} over \mathbb F_{{p}^{{m}}} are completely determined. In addition, we establish all MDS symbol-pair cyclic codes of length 2\textit {p}^{\textit {s}} over \mathbb F_{{p}^{{m}}} . Some MDS symbol-pair cyclic codes are better than all the known ones. Among others, we discuss possible applications to construct quantum MDS symbol-pair codes.