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The theory of error correcting codes is well developed, but that theory involves calculations in fields other than the ones which most people are used to. In order to do error correction it is necessary to do arithmetic in extension fields of the integers mod 2. This is a review of some techniques that are useful in performing the necessary calculation sin these fields. Only a working knowledge of polynomial rings will be assumed, and a detailed explanation of terms from abstract algebra will be given. For a review of polynomial rings see Chapter 3, Section 9, of "Topics in Algebra" by I.N. Herstein (1964).

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