php, 71 bytes

Result

WA

Code [DL]

<?php for(;$c=fgets(STDIN);){$j=sqrt(8*bindec($c)+1);echo 1^$j==$j%50;}

stdin

00000001
10011001
11011101
11010010
01000111
11110001
11010110
01001110
00100100
11101001
01111000
11011100
01000010
11010100
01101001
10001001
11100111
10001000
11111101
11010101
10111100
01011011
00010101
10111110
00000011
00001010
00011100
10111111
01110000
00000000
11111101
00011110
01110001
11100101
00010000
10100110
01001010
10101011
01000110
01000010
00101010
00000110
00110111
11001010
10100101
11111111
00101101
00001111
10101101
00100000

stdout

00101110010101010001100000011001111110101001110011

stderr

strace