Consider the $2-$dimensional parity check code, in which a block of bits is organized

in a table $($rows and columns$)$ and a parity bit is calculated for each row and column.

Consider a block of $mm$ data bits, there will be $m$ row parity bits and $m$ column

parity bits.

$($i$)$ What is the data rate in terms of information bits transmitted per coded bit? Is

there more or less redundancy in this code compared to the one$-$dimensional

single$-$bit parity check code with the same number of data bits?

$(2$ marks$)$

$($ii$)$ For $m=3,$ what is the minimum Hamming distance of the set of codewords?

$(4$ marks$)$

$($iii$)$ What is the minimum Hamming distance for general $m?$

$(2$ marks$)$