Polynomial code

In coding theory, a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length) that are divisible by a given fixed polynomial (of shorter length, called the generator polynomial).

Fix a finite field ${\displaystyle GF(q)}$, whose elements we call symbols. For the purposes of constructing polynomial codes, we identify a string of ${\displaystyle n}$ symbols ${\displaystyle a_{n-1}\ldots a_{0}}$ with the polynomial

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