Application in Coding Theory
The reciprocal polynomial finds a use in the theory of cyclic error correcting codes. Suppose xn - 1 can be factored into the product of two polynomials, say xn - 1 = g(x)p(x). When g(x) generates a cyclic code C, then the reciprocal polynomial p*(x) generates C⊥, the orthogonal complement of C. Also, C is self-orthogonal (that is, C ⊆ C⊥), if and only if p*(x) divides g(x).
Read more about this topic: Reciprocal Polynomial
Famous quotes containing the words application and/or theory:
“The main object of a revolution is the liberation of man ... not the interpretation and application of some transcendental ideology.”
—Jean Genet (1910–1986)
“Won’t this whole instinct matter bear revision?
Won’t almost any theory bear revision?
To err is human, not to, animal.”
—Robert Frost (1874–1963)