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I'm considering a binary error-correction scheme, but I'm missing the correct terms to dig further into it.

The idea is to decide the code-rate during encoding, but for the decoder to decide how that's used, depending on its resources (and estimate of the actual transmission error rate).

For example, let's say our code rate is 0.8. 4 bits of input produces 5 bits of output, and we can detect single-bit errors or correct single-bit erasures.

But given 30 bits of the same output stream (24 bits of data) we should be able to detect two-bit errors and correct single-bit errors or two-bit erasures, at the cost of decoder complexity. And so on - considering longer sequences should let you correct more errors, even when they're adjacent.

Is there a name for this set of requirements, or a class of code that solves them?

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