Gaussian Eliminate for GF2 code - php

Question

I have this gauss_eliminate function, but instead of dealing with real numbers, I want it to work on binary values.
I need the GF2 gauss_eliminate function, where the input is binary and the output is binary.
This produces real values, not binary, eg
0.57142857142857
0.71428571428571
-0.42857142857143
-0.28571428571429
0.14285714285714
Gaussian elimination has these 3 allowed steps:
1) Swapping two rows (for achieving a certain look)
2) Multiplying a row by a nonzero number,
3) Adding a multiple of one row to another row.
-- in GF2: addition operation is XOR : 0+0=0, 0+1=1, 1+0=1, 1+1=0 --and--
multiplication is AND operation: 0*0=0,0*1=0,1*0=0,1*1=1
function gauss_eliminate($A, $b, $N)
{
for ($col = 0; $col < $N; $col++) {
$j = $col;
$max = $A[$j][$j];
for ($i = $col + 1; $i < $N; $i++) {
$tmp = abs($A[$i][$col]);
if ($tmp > $max) {
$j = $i;
$max = $tmp;
}
}
swap_rows($A, $b, $col, $j);
for ($i = $col + 1; $i < $N; $i++) {
$tmp = $A[$i][$col] / $A[$col][$col];
for ($j = $col + 1; $j < $N; $j++) $A[$i][$j] -= $tmp * $A[$col][$j];
$A[$i][$col] = 0;
$b[$i] -= $tmp * $b[$col];
}
}
$x = array();
for ($col = $N - 1; $col >= 0; $col--) {
$tmp = $b[$col];
for ($j = $N - 1; $j > $col; $j--) $tmp -= $x[$j] * $A[$col][$j];
$x[$col] = $tmp / $A[$col][$col];
}
return $x;
}
new code #1, still doesn't work:
function gauss_eliminate($A, $b, $N)
{
for ($col = 0; $col < $N; $col++) {
$j = $col;
$max = $A[$j][$j];
for ($i = $col + 1; $i < $N; $i++) {
$tmp = abs($A[$i][$col]);
if ($tmp > $max) {
$j = $i;
$max = $tmp;
}
}
swap_rows($A, $b, $col, $j);
for ($i = $col + 1; $i < $N; $i++) {
for ($j = $col + 1; $j < $N; $j++)
$A[$i][$j]=( $A[$i][$j] != $A[$col][$j] ) ? 1 : 0;
$A[$i][$col] = 0;
$b[$i]=( $b[$i] != $b[$col] ) ? 1 : 0;
}
}
$x = array();
for ($col = $N - 1; $col >= 0; $col--) {
# $tmp = $b[$col];
# for ($j = $N - 1; $j > $col; $j--) $tmp -= $x[$j] * $A[$col][$j];
$x[$col] = ( $x[$col] != $A[$col][$j] ) ? 1 : 0;
}
return $x;
}
New code #2 - still doesn't work - tmp setup to alternate
function gauss_eliminate($A, $b, $N)
{
for ($col = 0; $col < $N; $col++) {
$j = $col;
$max = $A[$j][$j];
for ($i = $col + 1; $i < $N; $i++) {
$tmp = abs($A[$i][$col]);
if ($tmp > $max) { $j = $i; $max = $tmp; }
}
swap_rows($A, $b, $col, $j);
for ($i = $col + 1; $i < $N; $i++) {
# $tmp = $A[$i][$col] / $A[$col][$col];
for ($j = $col + 1; $j < $N; $j++) $A[$i][$j]=($A[$i][$j] != $A[$col][$j] ? 1 : 0);
$A[$i][$col] = 0;
$b[$i] = ( $b[$i] != $b[$col] ? 1 : 0);
}
}
$x = array();
for ($col = $N - 1; $col >= 0; $col--) {
$tmp = $b[$col];
for ($j = $N - 1; $j > $col; $j--) $tmp = 1 - $tmp;
$x[$col] = ($tmp != $A[$col][$j] ? 1 : 0);
}
return $x;
}

Answer 1

It appears I found the right syntax. I am getting the right result for one example, after modifying the code in a way that makes sense.... converting - to +, and this + to XOR, while / is ignored and * is AND.
Still it would be nice to get a confirmation that this code is correct.
function gauss_eliminate($A, $b, $N) {
for ($col = 0; $col < $N; $col++) {
$j = $col;
$max = $A[$j][$j];
for ($i = $col + 1; $i < $N; $i++) {
$tmp = abs($A[$i][$col]);
if ($tmp > $max) {
$j = $i;
$max = $tmp;
}
}
swap_rows($A, $b, $col, $j);
for ($i = $col + 1; $i < $N; $i++) {
# $tmp = $A[$i][$col] / $A[$col][$col];
# for ($j = $col + 1; $j < $N; $j++) {
# $A[$i][$j] -= $tmp * $A[$col][$j];
# }
# $A[$i][$col] = 0;
# $b[$i] -= $tmp * $b[$col];
$tmp = $A[$i][$col];
for ($j = $col + 1; $j < $N; $j++) {
# $A[$i][$j] = $A[$i][$j] + ( $tmp * $A[$col][$j] );
$A[$i][$j] = ( $A[$i][$j] != ( $tmp && $A[$col][$j] ) ) ? 1 : 0;
}
$A[$i][$col] = 0;
# $b[$i] = $b[$i] + ($tmp * $b[$col]);
$b[$i] = ( $b[$i] != ($tmp && $b[$col]) ) ? 1 : 0;
}
}
$x = array();
for ($col = $N - 1; $col >= 0; $col--) {
$tmp = $b[$col];
for ($j = $N - 1; $j > $col; $j--) {
# $tmp -= $x[$j] * $A[$col][$j];
# $tmp = $tmp + ($x[$j] * $A[$col][$j]);
$tmp = ( $tmp != ($x[$j] && $A[$col][$j]) ) ? 1 : 0;
}
# $x[$col] = $tmp / $A[$col][$col];
$x[$col] = $tmp;
}
return $x;
}
The commented text is the old (non GF2 code) as well as my "middle step" of showing where I convert + to XOR, * to AND, etc