That bitwise XOR is polynomial addition (and subtraction) in F_2[x] (polynomials with coefficients mod 2)? More immediately, it’s about the only way to unambig

That bitwise XOR is polynomial addition (and subtraction) in F_2[x] (polynomials with coefficients mod 2)? More immediately, it’s about the only way to unambiguously write which polynomial you mean, independent of endianness and similar notational issues. (The error correction properties don’t care about the way you arranged the bitstream into bytes or words.) But I find the knowledge that I am just implementing long division helpful, too. I did transcribe the beast mindlessly from a reference book a couple of times before I got it, but debugging it that way is pure hell.