A study showing that if Bose-Chaudhuri type parity check matrices are augmented by one or two columns, the corresponding codes--constructed by means of Galois fields--not only can correct a predetermined number of independent errors but also can correct bursts of errors that may occur in message transmission. In using such codes, it is necessary to add redundancy to the code messages, that is, to add "check places" to the original message that do not give any additional information. Thus redundancy is the price for sending a correct message, and the question then becomes one of how to obtain codes having a minimum amount of redundancy for a given message length, and still ensure that although a transmitted message may contain one or more bursts of errors, it will still be decoded correctly. These codes are extensions of the Bose-Chaudhuri codes, dealing with independent error correction. 48 pp. Ref.