OPTIMUM BINARY CYCLIC BURST CORRECTING CODES.

Summary form only given. A code is called a b-burst correcting code if it can correct any single cyclic burst of length b or less. The length n and redundancy r of a binary b-burst correcting code satisfy n less than equivalent to 2**r- **b** plus **1 - 1. A binary b-burst correcting code which satisfies this bound with equality is said to be optimum. It is proved that for every positive integer b, for every square-free polynomial e(x) over GF(2) of degree b - 1 which is not divisible by x, and for every sufficiently large m is identical to O(mod m//e ), where m//e is the least common multiple of the degrees of the irreducible factors of e(x), there exists a primitive polynomial p(x) over GF(2) of degree m such that e(x)p(x) generates an optimum b-burst correcting code of length 2**m equals 1. This implies that for every positive integer b, there exists infinitely many optimum binary cyclic b-burst correcting codes.