Optimal values of mxn matrix

I have 3840 bits which I want to arrange in a mxn matrix. This is for a hybrid ARQ scheme which will be used to correct errors. After arranging the bits in a matrix, sum of all the ones in a row,are appended to the row as parity bits and for every column, odd/even parity bits are added. Now the HARQ mechanism can correct at the most one error per column and for the rows, the logic is that if all the errors are the same, then they can be corrected. For eg. if the transmitted bits in a row were 1001 and the received bits were 1111, ie 2nd and 3rd bit in error, but the same error, then the row can be corrected. If for the same transmitted bit sequence, the received bits were 0101, ie.first and second bit in error, then this error can't be corrected as the values are different. The point is, that my on air overheads need to be as small as possible...overheads here being the row and column parities being added. So what should be the optimal size of the mxn matrix with the given error correcting constraints?

[José-Luis]

What have you tried so far?

[the cyclist]

I don't see a MATLAB question here.