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as 12 -> 21
* twin errors, such as 11 -> 22
* jump transpositions errors, such as 132 -> 231
* jump twin errors, such as 131 -> 232
* phonetic errors, such as 60 -> 16 ("sixty" to "sixteen")

In choosing a system, a high probability of catching errors is traded off against implementation difficulty; simple check digit systems are easily understood and implemented by humans but do not catch as many errors as complex ones, which require sophisticated programs to implement.

A desirable feature is that left-padding

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