primitive polynomial

Noun

Meaning

(algebra, ring theory) A polynomial over an integral domain R such that no noninvertible element of R divides all its coefficients at once; (more specifically) a polynomial over a GCD domain R such that the greatest common divisor of its coefficients equals 1.

(algebra, field theory) A polynomial over a given finite field whose roots are primitive elements; especially, the minimal polynomial of a primitive element of said finite field.

Related terms

Examples

The feedback tap numbers in white correspond to a primitive polynomial in the table so the register cycles through the maximum number of 65535 states excluding the all-zeroes state. Source: Internet

The register numbers in white correspond to the same primitive polynomial as the Fibonacci example but are counted in reverse to the shifting direction. Source: Internet

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