Q66

Data transmitted on a link uses the following $2D$ parity scheme for error detection: Each sequence of $28$ bits is arranged in a $4\times 7$ matrix (rows $r_0$ through $r_3$, and columns $d_7$ through $d_1$) and is padded with a column $d_0$ and row $r_4$ of parity bits computed using the Even parity scheme. Each bit of column $d_0$ (respectively, row $r_4$) gives the parity of the corresponding row (respectively, column). These $40$ bits are transmitted over the data link.

$$\small \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline &\bf{d_7}&\bf{d_6}&\bf{d_5}&\bf{d_4}&\bf{d_3}&\bf{d_2}&\bf{d_1}&\bf{d_0}\\ \hline \bf{r_0}&0&1&0&1&0&0&1&\bf{1}\\\hline \bf{r_1}&1&1&0&0&1&1&1&\bf{0}\\\hline \bf{r_2}&0&0&0&1&0&1&0&\bf{0}\\\hline \bf{r_3}&0&1&1&0&1&0&1&\bf{0}\\\hline \bf{r_4}&\bf{1}&\bf{1}&\bf{0}&\bf{0}&\bf{0}&\bf{1}&\bf{1}&\bf{0}\\ \hline\end{array}$$

The table shows data received by a receiver and has $n$ corrupted bits. What is the mini­mum possible value of $n$?