Burst and unidirectional error detecting codes

It is proved that codes devised by J. Berger (see Inf., and Control. vol.4, p.68-73, (1961)) that detect random bursts of length b and simultaneously detect any number of unidirectional errors (b-bED/AUED codes) are optimal. The construction is modified in two ways: (1) to obtain b-bED/s-UED codes in which a random burst of length b and up to s unidirectional errors are detected, and (2) to obtain b-bED/s-UbED codes in which a random burst of length b and a unidirectional burst of length s are detected. A lower bound on the number of check bits for such codes is obtained. The lower bounds indicate that the proposed b-bED/s-UED codes are close to optimal and the b-bED/s-UbED codes are asymptotically optimal.<>