Abstract Algebra: Theory and Applications · Problem 22.4.28

Galois Theory — Thomas Judson

Mathematics — Abstract Algebra · finite-fields-cyclic-codes

Problem

Let CC be a code in RnR_n that is generated by g(t)g(t). If ⟨f(t)⟩\langle f(t) \rangle is another code in RnR_n, show that ⟨g(t)⟩⊂⟨f(t)⟩\langle g(t) \rangle \subset \langle f(t) \rangle if and only if f(x)f(x) divides g(x)g(x) in Z2[x]\mathbb{Z}_2[x].

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