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Reed–Solomon Codes for Coders
codes for coders Error correcting codes are a signal processing technique to correct errors. They are nowadays ubiquitous, such as in communications (mobile phone, internet), data storage and archival (hard drives, optical discs CD/DVD/BluRay, archival tapes), warehouse management (barcodes) and advertisement (QR codes).
The bits after that can be rearranged in bytes representing the actual characters of the messageː 27 54 77 61 73 20 62 72 69 6c 6c 69 67, and additionally 0e c. The first two, hex 27 and 54 are the ASCII codes for apostrophe and T. The whole message is "'Twas brillig" (from w:Jabberwocky#Lexicon). (Note that Reed–Solomon is also based on this principle, but since the number of possible codewords is simply too big, we can't afford to do an exhaustive search, and that's why clever but complicated algorithms have been devised, such as Berlekamp-Massey.) There are some ways to optimize the speed by using various tricks, such as inlining (instead of gf_mul, replace by the operation to avoid a call), by precomputing (the logarithm of gen and of coef, or even by generating a multiplication table – but it seems the latter does not work well in Python), by using statically typed constructs (assign gf_log and gf_exp to array.array('i', [...])), by using memoryviews (like by changing all your lists to bytearrays), by running it with PyPy, or by converting the algorithm into a Cython or a C extension[1].
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