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

Algorithm 2

Finding the optimized bitmatrix of PB-MBR (the algorithm first denotes a set of and each and finds the best 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 to construct and count
(4)	as the set of diagonal matrices and each matrix form from multiplcative inverses of
(5)	for each do
(6)
(7)	Count
(8)	end for
(9)	Choose the best which has the min
(10)	The column of the matrix with all number 1 is
(11)	The set includes all columns except column
(12)	for each column do
(13)	for each row to do
(14)	for each row to do
(15)	Calculate
(16)	end for
(17)	Count of this new column
(18)	end for
(19)	Choose the column with min as new column of
(20)	end for
(21)	Choose columns with the min to construct
(22)	Count