Title :
On the existence of optimum cyclic burst correcting codes over GF( q)
Author :
Abdel-Ghaffar, Khaled A S
Author_Institution :
Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA
fDate :
3/1/1988 12:00:00 AM
Abstract :
A cyclic b-burst correcting code over GF(q) of redundancy r and length n=(qr-b+1-1)/(q-1) is said to be optimum. It is proved that a necessary condition for the existence of such a code is the existence of a square-free polynomial in GF(q)[x] of degree b-1 which is not divisible by x such that its period and the degrees of its irreducible factors are relatively prime to q-1. Moreover, if such a polynomial exists, then there are an infinite number of optimum cyclic b-burst correcting codes over GF(q)
Keywords :
error correction codes; b-burst correcting code; optimum cyclic burst correcting codes; redundancy; square-free polynomial;
Journal_Title :
Information Theory, IEEE Transactions on