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There's a QR code in 16-cubes city but it has been blocked by some obstacle.

in-game incomplete image

And I tried to fix the picture to make it clearer but there's still something missing in the top left part.

removed the scaffolding blocking parts of the code

You can clean that up further and replace the missing parts that are unfinished but known:

black-and-white QR code with some missing pixels placed

But it still doesn't scan.

Does anyone have any ideas about this?

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As a note, you can't just "clean up" and "replace missing parts" of 2d and barcodes. That's encoded information, swapping one pixel can change the contained information of the code. Reconstruction of damaged (like this one) 2d and barcodes is hard and more of brute force nature. –  Bobby Apr 15 '12 at 11:21
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@Bobby: It's missing less than one quarter, most of which was the position, format, and timing indicators, all of which are redundant data and can easily be replaced. The remaining missing data comprises an easily brute-forceable number of bits. At minimum a QR code can have 7% of its words corrupted and still be perfectly recoverable. –  user2640 Apr 15 '12 at 12:28
    
After you start a new game plus you get an extra ability that'll help with viewing the obstructed codes! –  user26632 May 30 '12 at 15:53
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3 Answers

The 16-cube area is the ancient version of the temple/science warp zone. That QR code was under construction long ago, but it now appears "fully realized" on the same wall in the temple/science warp zone. So it can be completed—indeed, it has been.

QR code from temple/science warp zone

If you're curious, the QR code links to...

text: "RT RT LT RT LT LT LT RT" (which triggers an anticube, as shown above)

This is a higher resolution of the screenshot, from the PC gersion of the game: Complete QR code on a screenshot

I have then extracted the QR code, converted it to black and white, removed Gomez and some dust, and applied a median filter. This is the complete QR code, which you can scan on a website.

Complete QR code extracted

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Are you sure it can't be completed? The number of missing elements is very small and all the format data is available. Seems like we're missing maybe 20-30 bits... –  user2640 Apr 15 '12 at 10:20
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It isn't meant to be completed by us—it's more of a plot continuity thing –  Sean Apr 15 '12 at 10:27
    
This QR Code is linked to the Monocle Room (Fezzes Painting) in the first village. –  Gimlao Apr 17 '12 at 12:31
    
How do you read this QR code? I cannot get anything from mine. –  Wok May 2 '13 at 22:11
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Okay, I had to resize the QR code so that it fits in 400x400 pixels. This was my problem: the high resolution of a PC screenshot. This website gives the result: scanner.code-qr.net –  Wok May 2 '13 at 22:32
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I finished the game and found the completed QR code. After I scanned it it's #F0493E, which is a hex color for a shade of red. I want to say it has something to do with the 3 red rooms and the 3 missing pieces of the heart puzzle...but I have no way of proving that.

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The code translates to RT RT LT RT LT LT LT RT. If you push d d a d a a a d you get an anticube

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