vim, 158 bytes

Result

AC

Code [DL]

00000000  71 7a 22 61 78 22 62 78  22 63 78 22 64 78 22 65  |qz"ax"bx"cx"dx"e|
00000010  78 22 66 78 22 67 78 22  68 73 12 3d 70 6f 77 28  |x"fx"gx"hs.=pow(|
00000020  66 6c 6f 6f 72 28 73 71  72 74 28 28 40 61 2a 31  |floor(sqrt((@a*1|
00000030  32 38 2b 40 62 2a 36 34  2b 40 63 2a 33 32 2b 40  |28+@b*64+@c*32+@|
00000040  64 2a 31 36 2b 40 65 2a  38 2b 40 66 2a 34 2b 40  |d*16+@e*8+@f*4+@|
00000050  67 2a 32 2b 40 68 29 2a  38 2b 31 29 29 2c 32 29  |g*2+@h)*8+1)),2)|
00000060  3d 3d 28 40 61 2a 31 32  38 2b 40 62 2a 36 34 2b  |==(@a*128+@b*64+|
00000070  40 63 2a 33 32 2b 40 64  2a 31 36 2b 40 65 2a 38  |@c*32+@d*16+@e*8|
00000080  2b 40 66 2a 34 2b 40 67  2a 32 2b 40 68 29 2a 38  |+@f*4+@g*2+@h)*8|
00000090  2b 31 0a 1b 6a 5e 71 34  39 40 7a 5a 5a 0a        |+1..j^q49@zZZ.|
0000009e

Disassembly

qz"ax"bx"cx"dx"ex"fx"gx"hs<C-R>=pow(floor(sqrt((@a*128+@b*64+@c*32+@d*16+@e*8+@f*4+@g*2+@h)*8+1)),2)==(@a*128+@b*64+@c*32+@d*16+@e*8+@f*4+@g*2+@h)*8+1<NL><Esc>j^q49@zZZ<NL>

stdin

01111100
11000011
10011110
00101101
11000001
10110110
00001010
11100111
01001100
00001111
00001000
10001110
11111101
01001010
00000110
10111110
01000010
11001111
00011100
10001010
00110111
10110000
00100100
00000000
11010010
11101000
10011101
10001001
00000001
01000101
10101011
10001000
10011001
11000111
01001110
10001000
00110101
10000000
11111001
00000011
01011011
01101001
01010010
01111000
00001110
01101111
10100000
11010111
00010101
00000000

stdout

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stderr

strace