Algorithm 7.

[combinations] = RADIXSORT(R⁽¹⁾, combinations, width)

Input:
	R(1) – bit pattern matrix used to generate new candidates
	combinations – pairs of column indices which generate new candidates
	width – width of the sequence of bits over which elementary radix sort is performed
Output:
	combinations – reordered pairs of indices so that corresponding columns are sorted
1:	r ⇐ size(R(1), 1)
2:	col_length ⇐ number of machine words in r bits
3:	for i = 1 to col_length do
4:	factor ⇐ $\frac{\text{r}}{\text{width}}$ {number of sequences of length width in current word}
5:	for j = 1 to factor do
6:	counting ⇐ zeros (1, 2width)
7:	for k = 1 to length(combinations) do
8:	(ii, jj) ⇐ combinationsk
9:	aa ⇐ ${\text{R}}_{\ast ,\text{ii}}^{(1)}$ or ${\text{R}}_{\ast ,\text{jj}}^{(1)}$
10:	aa ⇐ (aa shl j · width) and (2width − 1)
11:	countingaa ⇐ countingaa + 1
12:	end for
13:	for k = 1 to 2width do
14:	countingk ⇐ countingk + countingk−1
15:	end for
16:	for k = length(combinations) downto 1 do
17:	(ii, jj) ⇐ combinations(k)
18:	aa ⇐ ${\text{R}}_{\ast ,\text{ii}}^{(1)}$ or ${\text{R}}_{\ast ,\text{jj}}^{(1)}$
19:	aa ⇐ (aa shl j · width) and 2width − 1
20:	combinations_sorted[countingaa − 1] ⇐ combinationsk
21:	countingaa ⇐ countingaa − 1
22:	end for
23:	combinations ⇐ combinations_sorted
24:	end for
25:	end for