A Class of Convolution Codes

This paper describes a class of infinite convolution codes which are designed to minimize the time required to recover from an erasure burst on the binary erasure channel. It is shown that for any given rate, there exists a unique optimum erasure burst correcting code. For rates of the restricted form R = n /( n + 1), an algorithm is given by which the code of this rate may be written down by inspection. For other rates, the codes can be determined by a more complicated procedure based on evaluating large binary determinants.