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Inspired by a post about car park identifiers, I started wondering if we could avoid two adjacent car parks having identifiers which could easily be mistaken for each other:

What are the best arrangements of all the decimal numbers of a certain length are there that have the property that for each number, a single replacement or adjacent transposition does not occur in the list within X numbers.

(for example: 142 should not be near 172 (single replacement) nor 124 (adjacent transposition))

(I'm pretty happy with alternatives that have other criteria for typo-resistance)

Prior art

Gray code has the nice property that every number shares all-but-one (binary) digits; this feels like the opposite property of what I want.

David McKee
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  • You need to be more specific about what properties you want, but you may be looking for something closer to a Hamming code (with error correcting properties) than a Gray code. – Henry Nov 27 '23 at 12:15
  • I'm not sure Hamming codes are right -- that seems to be about adding digits within a single identifier to ensure correct reception, whereas I'm hoping that within a finite space of numbers (which may all be used) to space out the nearly-colliding ones. – David McKee Nov 27 '23 at 12:32

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