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).
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