TY - GEN

T1 - OPTIMUM BINARY CYCLIC BURST CORRECTING CODES.

AU - Abdel-Ghaffar, Khaled A S

AU - McEliece, Robert J.

AU - Odlyzko, Andrew M.

AU - Van Tilborg, Henk C A

PY - 1986/12/1

Y1 - 1986/12/1

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:0022989975

BT - Unknown Host Publication Title

PB - IEEE

ER -