Analysis of recurrent codes

A definition of a recurrent code is given in a framework which renders it amenable to mathematical analysis. Recurrent codes for both independent and burst errors are considered, and a necessary and sufficient condition for either type of error correction is established. For burst-error-correcting codes, the problem treated is (for a fixed burst length and redundancy) the minimization of the error-free distance ("guard space") required between bursts. A lower bound is obtained on the guard space, and in certain cases, codes which realize this bound are given. A general code which is close to the lower bound in many cases is also given. For independent errors, a code which will correct any error, provided that no consecutive " n " positions have more than " e " digits in error, is discussed. For e = 1 , a necessary and sufficient condition on n is derived; for e > 1 , a lower bound on n is obtained, and for the case of redundancy 1/2 , an upper bound on n is also derived.