csharp, 133 bytes

Result

WA

Code [DL]

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

stdin

00001010
10110010
11100001
00001111
01101010
11111100
01000011
00110111
01111001
10101011
11010010
00100011
00000011
00001100
00001101
00000001
01001110
10101011
11111011
00010000
00011110
00000110
11110011
00011100
10010101
10010111
01011001
00000000
10110011
11111101
11100111
10111110
00101010
11011101
00101101
01000000
01110101
10001100
10011110
10001000
00010101
00100100
01000010
01111110
01111000
00000110
10011001
01011011
11011110
01101001

stdout

Compilation failed: 1 error(s), 0 warnings

stderr

/tmp/code.cs(1,75): error CS0103: The name `Sqrt' does not exist in the current context
Cannot open assembly '/tmp/code.exe': No such file or directory.
rm: cannot remove '/tmp/code.exe': No such file or directory

strace