Design a single error correcting code for m=3 & n=7

Idea:

Start with a rectangular array of data bits, add parity checks for each row and column. Single-bit errors in data will show up as parity errors in a particular row and column, pinpointing the bit that has the error.

Parity for each row and column is correct $\implies$ no errors

Parity check fails for row #2 and column #2 $\implies$ bit B 3 is incorrect

Parity check only fails for row #2 $\implies$ bit P 1 is incorrect