Night 055Kästchen

Night fifty-five, a piece night, and the rotation pointed at a tool. The QR code maker had sat in the backlog since the first week with the note “implement the encoder yourself, no library”. Kästchen means little boxes, which is what a QR symbol is: a few thousand of them, each one meaning something.

That meaning is the point. Most QR makers hand you the picture. This one shows the construction. A scrubber walks through the symbol in the order the standard builds it: the three finders with their white separators, the timing lines, the alignment patterns, the one module that is always dark, the areas reserved for format and version information, and then the codewords, placed one byte at a time along the zigzag that climbs and descends in two-module columns. Data and error-correction codewords are tinted by block, so the interleaving is visible. Then the mask, and last the format bits. Hover a module and it tells you what it is.

Underneath is a complete encoder: numeric, alphanumeric and byte modes, all forty versions, four error-correction levels, Reed–Solomon over GF(256) with the generator polynomials computed at load, the eight masks scored by the four penalty rules, and the BCH codes for format and version information. Nothing leaves the page. The symbol exports as SVG or PNG, and the text and settings live in the link.

Claude Opus 5.5 built it from my spec in two rounds. Correctness was the whole risk, so the harness checks the standard’s worked example, the known format and version words, and a rule I like: for every version, the codewords in the block table must add up to exactly the modules left after the function patterns, divided by eight. Then an independent decoder read back every version at every level. Two things went wrong in a useful way. One test vector in my spec was wrong, and the builder proved it with the BCH arithmetic instead of bending the code to match. And version 23 at level L would not decode: the decoder library carries a wrong alignment coordinate for that version, and at the other three levels the error correction had quietly absorbed it. My own review found the layout folding the symbol to a stamp between 800 and 1100 pixels wide; round two fixed that.

Safari and Firefox are untested, as usual.