How QR codes work.

Why the three corners look weird

The 1:1:3:1:1 ratio of black-white-black-white-black in the finder patterns is deliberately rare. If you scan a single line across one, you get those specific run lengths. The scanner sweeps the image looking for exactly that pattern in any orientation; when it finds three of them in roughly an L shape, it knows where the code is and which way is up. The reason QR codes work upside down is that those three corners pin the orientation.

Why Reed-Solomon and not just a checksum

A checksum tells you something is wrong; it can\'t tell you what. Reed-Solomon, with the right amount of redundancy, both detects and locates errors and then corrects them. That\'s why a torn corner doesn\'t kill a QR code: the algorithm reads the surviving 196 modules, notices 12 don\'t agree with the polynomial check, computes where they went wrong, and fixes them.

The same code family powers CDs (handling scratches), DVDs, Blu-ray, satellite communications, and DNA storage prototypes. The structure stays the same; only the field sizes and ECC fractions change.

What the mask is actually doing

Without a mask, certain payloads would produce QR codes with big runs of one colour, or even patterns resembling the finder bullseyes elsewhere in the grid — and the scanner would get confused. The eight standard masks are simple deterministic functions (e.g. (row + col) % 2 == 0) that XOR with the data. The encoder generates all eight, scores each on four penalty criteria (run length, 2×2 blocks, finder-like sequences, light/dark ratio), and picks the lowest score. The mask choice goes into the format info so the decoder knows which one to undo.

What this visualisation simplifies

• Real bit values. Our data bits are pseudo-random for visual variety. The real encoded payload for "HI" is 0010 + 000000010 + 01100001111 + terminator + pad bytes. The visual structure is faithful.
• Format info bits. We grey-fill the format region instead of computing the real 15-bit BCH-encoded format word. Real format = ECC level (2 bits) + mask number (3 bits) + 10 BCH bits, then XORed with a fixed mask 101010000010010.
• Alignment patterns. V1 is the only version without them. From V2 up there are smaller 5×5 alignment patterns scattered to help scanners cope with curvature.
• Mask selection. We applied mask 0 directly. A real encoder generates all 8 masks, scores them, and picks the best.
• Reed-Solomon details. We say "decoder fixes 12 errors" without going through syndrome computation, error-locator polynomial, Chien search, and Forney\'s algorithm. The full math is its own page.

Why QR codes spread when others didn\'t

Datamatrix, PDF417, Aztec, MaxiCode — there are dozens of 2D barcode formats. QR won because (a) Denso Wave didn\'t enforce its patent, (b) the finder pattern is fast enough to detect on cheap CPUs, (c) error correction means smudged prints still scan, and (d) phone cameras + on-device decoders made the read free. The combination of "easy to print, hard to ruin, free to scan" beat every technically nicer alternative.