On the existence of optimum cyclic burst- correcting codes

It is shown that for each integer
b \geq 1
infinitely many optimum cyclic
b
-burst-correcting codes exist, i.e., codes whose length
n
, redundancy
r
, and burst-correcting capability
b
, satisfy
n = 2^{r-b+1} - 1
. Some optimum codes for
b = 3, 4
, and
5
are also studied in detail.