Australia Post, the postal code that repairs what it reads

[s2x]

The twenty-ninth generator, and the last of the four-state postal codes.

australia-post (aliases auspost, australia-post-4state, customer-barcode), pure PHP, one option.

What it is

An eight-digit sorting code — the Delivery Point Identifier — optionally followed by a customer information field. After Intelligent Mail the layout reads like a relief: start bars, Format Control Code, sorting code, customer field, parity, stop bars, every field at a fixed offset.

What it spends instead is the parity. It is the only postal code here that corrects: four Reed–Solomon codewords over GF(64), repairing two of them. Encoding\ReedSolomonGf2m already spoke that field for Aztec and MaxiCode, so this reused rather than grew. It is also why the bars group in threes — three bars are six bits are one codeword — and why the Standard Customer Barcode is thirty-seven bars rather than thirty-six: one filler bar exists so the count divides.

Two decisions

The Format Control Code is an option. Six codes exist. Three are what the article is — Reply Paid, Routing, Redirection — and nothing in the data says which was meant. The other three (11, 59, 62) are not a choice: they follow from the width of the customer field, so Payload picks them.

A half-filled customer field is refused, not padded. The field is sized in bars rather than characters, which is why the lengths look arbitrary and are not: 5 or 10 characters, or 8 or 15 digits. Padding a shorter one would mean inventing semantics no reader has agreed to — filler bars in the middle of a C-table field index as lower-case letters — and zint will not draw such a symbol for comparison either.

Both character tables are derived rather than transcribed. They turned out to be one enumeration read at two widths: combinations with no tracker bar first in ascending order, then those with a tracker in the leading bar, then the leftovers.

Verification

• 527 symbols bar for bar against zint (composer reference:australia-post), covering all six Format Control Codes and every character of both tables at the front, middle and back of both field widths.
• The fixture sweeps until all sixty-four parity codeword values have been drawn in all four parity positions — a generator polynomial right for three positions out of four is exactly what a fixture of chosen payloads misses.
• The parity is also checked by its definition: the test builds GF(64) from the primitive polynomial itself and asserts every symbol's syndromes are zero at α¹ to α⁴, which is an opinion that does not pass through the class that made the symbol.
• Rendered PNG measured back into bars, in DecoderRoundTripTest, with the family's standing no-free-decoder caveat and its expiry test.

Suite: 16103 tests, 269831 assertions. composer lint clean.