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The theory of error-correcting codes stems from Shannon's 1948 _A mathematical theory of communication_, and from Hamming's 1950 "Error detecting and error correcting codes".

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"Codes" in which a group of words are pairwise different at a certain position

I read the following problem, claimed to be in the IMO shortlist in 1988: A test consists of four multiple choice problems, each with three options, and the students should give an unique answer t …
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Block error-correcting codes over inhomogeneous alphabets

I think what you are looking for is mixed codes. A good start point would be Brouwer--Hämäläinen--Östergård--Sloane. They are talking about mixed binary/ternary code, so for some $k$, $n_1=\cdots=n_k …
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