csharp, 135 bytes

Result

WA

Code [DL]

using System;class {static void Main(){for(int i=51;--i;)Console.Write(Math.Sqrt(8*Convert.ToByte(Console.ReadLine(),2)+1)%2==1?1:0);}}

stdin

10001000
00100100
10011110
10011001
00000011
11010101
10011100
00000000
11001011
11111101
01000100
00000001
01111011
00000000
11011000
11000011
11010011
01001110
01001100
00001111
00111011
10101011
01000010
01010010
00101101
11001001
11011110
00000110
01011011
11110100
00001010
00000000
00110111
10111110
01011100
00011100
10011011
00100111
01111000
01100001
00010101
01101001
11111100
01000011
10110111
10101001
01011110
11010010
11100111
11101100

stdout

Compilation failed: 1 error(s), 0 warnings

stderr

/tmp/code.cs(1,19): error CS1001: Unexpected symbol `{', expecting identifier
Cannot open assembly '/tmp/code.exe': No such file or directory.
rm: cannot remove '/tmp/code.exe': No such file or directory

strace