How Many Digits Does a Local Postal Code Need? Capacity, Growth Headroom, and a Check Character That Catches Copying Errors
Year: 2026
Type: article
Abstract: A local postal code introduced for one settlement must do three jobs: name every household, leave room to grow, and betray its own copying errors. This paper sizes the code for a settlement of 8500 households with a stated growth factor of 1.8 over the planning horizon and a quarter of the code space held in reserve: 20400 codes are required, so 5 digits — capacity 100000, a headroom of 4.9 times — plus one check character, for a total length of 6. The check character, a weighted mod-11 sum, was verified by exhaustive testing rather than asserted: all 180000 single-digit errors in the test set were caught, and all 14410 adjacent transpositions were caught. A sizing table for settlements from 500 to 120000 households shows digits growing by one per tenfold of population, which is why a code sized for a town must never be borrowed from a village. SIMULATED, NOT MEASURED.
Author: Aldred, William Alexander
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225734959
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