Symbol-pair codes: Algebraic constructions and asymptotic bounds

For the recently proposed model of symbol-pair channels, we advance the pair-error coding theory with algebraic cyclic-code constructions and asymptotic bounds on code rates. Cyclic codes for pair-errors are constructed by a careful use of duals of known tools from cyclic-code theory. Asymptotic lower bounds on code rates show that codes for pair-errors provably exist for rates strictly higher than codes for the Hamming metric.