PB: A Product-Bitmatrix Construction to Reduce the Complexity of XOR Operations of PM-MSR and PM-MBR Codes over

Algorithm 1

Finding the optimized bitmatrix of PB-MSR (the algorithm first gets a new which has a minimal number of ones and then finds which has minimal number of ones).

(1)	is the number of ones of a matrix;
(2)	is the number of ones of the column;
(3)	Use Cauchy matrix construct and count ;
(4)	for each column to do
(5)	for each row to do
(6)	for each row to do
(7)	Calculate ;
(8)	Count of this new column;
(9)	end for
(10)	end for
(11)	Choose the column with min as new column of ;
(12)	end for
(13)	Construct and each column has min;
(14)	Count ;
(15)	for each column to do
(16)	for each row to do
(17)	;
(18)	for each column to do
(19)	;
(20)	end for
(21)	end for
(22)	if is inverse then
(23)	Count ;
(24)	else
(25)	repeat 16–26 steps by multiplying the power of ;
(26)	end if
(27)	end for
(28)	Choose the best which has the min;