Burst errors are very common, in particular in wireless environments where a fade will affect a group of bits in transit. The length of the burst is dependent on the duration of the fade.
One way to counter burst errors, is to break up a transmission into shorter words and create a block (one word per row), then have a parity check per word.
The words are then sent column by column. When a burst error occurs, it will affect 1 bit in several words as the transmission is read back into the block format and each word is checked individually.
Using Polynomials
We can use a polynomial to represent a binary word.
Each bit from right to left is mapped onto a power term.
The rightmost bit represents the “0” power term. The bit next to it the “1” power term, etc.