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Generally speaking most QR codes look as though they have about 50% of their cells black. If a putative QR code had 90% or 10% of its cells black, we would reasonably conclude that it didn't look like a QR code. Centred on the mean, which may possibly not be 50%, in what interval must the percentage of black squares fall in order to capture 95%, 99%, and 99.9% of possible QR codes? I intend "possible" to mean "appearing for normal purposes", which I realise is open-ended. If it is necessary to assume a certain size, please use version 1, which defines a 21 x 21 cell array.

  • Nice question. But very difficult to answer without full knowledge of BCH, Reed Solomon Codes and the QR standard in detail and then converting the QR print layout of that into b/w ratio on which you want interval stats.

    Having said that, are you hung up on getting a mathematical proof? If not, you could try an empirical approach with samples of QR codes and statistical analysis of the blact/white ratio of those. I am assuming this is not an exercise in theory and you want to solve this for addressing a practical problem.

     – vvg Oct 21 '20 at 18:53
  • Thanks for this. No, I don't need a mathematical proof but not knowing much about the QR standard I thought that might be an easier route because a sample would probably have to be of size $n\sim 10^4$ to yield a robust answer, at least for the $p=99.9%$ case. –  Oct 21 '20 at 19:07
  • Building a small program to generate even 10,000 barcode images along with image analysis statistics may be the way to go. Trying to model the QR standard might be an uphill task. The former might be quicker, relatively. Good luck with your effort. – vvg Oct 21 '20 at 19:21

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