The authors investigate the problem of evaluating the possible size of error-correcting codes with code words taken from a subset of Hamming spaces. This is an example of the problem of constructing codes in irregular subsets of Hamming spaces. The authors examine the theoretical restrictions on the parameters of error-correcting codes in the asymptotic case (semi-finite sequence) when the recursive digital sum is upper-bounded by some small constant. The bounds allow demonstration of the existence of long codes that have good error-correcting properties and that satisfy some restrictions that are natural for optical and magnetic recording.
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