polynomial basis

Noun

Meaning

(algebra, ring theory) A basis of a polynomial ring (said ring being viewed either as a vector space over the field of coefficients or as a free module over the ring of coefficients).

(algebra, field theory, cryptography, of a finite field) Specifically, a basis, of the form {1, α, ..., α}, of a finite extension Fq of a Galois field Fq, where α is a primitive element of Fq (i.e., a root of a degree-n primitive polynomial over Fq).

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