MDS Symbol-Pair Cyclic Codes of Length 2p^s over F<inf>p</inf>^m

Abstract

© 1963-2012 IEEE. Let p be an odd prime, s and m be positive integers. Cyclic codes of length 2ps over Fpm are the ideals (x-1i(x+1)j, where 0 ≤ i, j ≤ ps, of the principal ideal ring Fpm [x]/ x2ps-1. Using this structure, the symbol-pair distances of all cyclic codes of length 2ps over Fpm are completely determined. In addition, we establish all MDS symbol-pair cyclic codes of length 2ps over Fpm. 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.