Class of linear cyclic block codes for burst errors occurring in one-, two- and three-dimensional channels

Owing to various natural and man-made noise, burst errors occur in one-, two- and three-dimensional telecommunication channels. In the paper, a class of linear cyclic block codes, which can correct all burst errors occurring in these types of channels, is described. The codes devised make use of the statistical description of the channel and the estimates of the possible error patterns which may occur throughout the channel. This is achieved by describing a regular geometrical shape which may contain each of these possible error patterns individually. Several examples of these geometric shapes in one-, two- and three-dimensional channels are given. Once an appropriate shape is found, the codes may be generated with their generator matrix. Because of their ability to correct errors, not only in one-, but also in two- and three-dimensional channels, these codes may be used in applications other than telecommunications, such as pattern and shape recognition in robotics. Experience shows that the codes are highly efficient and have a particularly simple decoding scheme.