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Error-correcting codes

The concept

Why a scratched DVD still plays perfectly

A scratched disc still plays without a skip because it stores more than the song: extra numbers computed from that same data, used to spot and fix damage.

Those extra numbers are called error-correcting codes. If a few bits go missing or get flipped, the player treats it like a sudoku puzzle: enough of the picture is still there to work out exactly what the missing pieces must have been.