Single- and multiple-burst-correcting properties of a class of cyclic product codes

The direct product of
p
single parity-check codes of block lengths
n_1,n_2, \cdots ,n_p
is a cyclic code of block length
n_1 \times n_2 \times \cdots \times n_p
with
(n_1 - 1) \times (n_2 - 1) \times \cdots \times (n_p - 1)
information symbols per block, if the integers
n_1,n_2 \cdots ,n_p
are relatively prime in pairs. A lower bound for the single-burst-correction (SBC) capability of these codes is obtained. Then, a detailed analysis is made for
p = 3
, and it is shown that the codes can correct one long burst or two short bursts of errors. A lower bound for the double-burst-correction (DBC) capability is derived, and a simple decoding algorithm is obtained. The generalization to correcting an arbitrary number of bursts is discussed.