Upon reading the Wikipedia article on bar codes, I learned that there is wide collection of 2D and linear bar codes. One format that I am familiar with is the QR Code.
What is the maximum storage capabilities of linear and 2D bar codes?
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First, it kind of depends on what you mean by “capacity”. For example, Eric J. is correct that the maximum capacity of a QR code in byte mode is 2953 bytes, for a version 40 code. However if your data is purely numeric, it can encode 7089 digits, as it has a special compressed encoding.
Second it’s important to realize that not all formats encode arbitrary data. For example there’s no notion of storing anything but a 12-digit numer in a UPC-A code. Code 128 can’t store arbitrary bytes. So some formats may be out of consideration depending on your use case.
Third the capacity can vary based on other choices, like error correction level.
Finally, importantly, there’s a big difference between the theoretical maximum capacity and the practical maximum. Yes, you can create a version 40 code, but good luck scanning it with a camera phone:
(original source).
It may work in the industrial contexts for which QR codes were originally designed, but not for consumer uses. Anything above version 10 (a few hundred bytes) gets hard to scan. In practice, sticking to version 5 or below is well advised (a hundred bytes or so).
The same is generally true of other formats. There are not big differences among 2D formats in this regard. At some level all are challenged by the same limitation of focus, CCD responsiveness, a motion blur.