Idempotent Polynomials: An Easy Supplant to Generator Polynomials
نویسندگان
چکیده
Cyclic codes are very useful in error correcting codes. Hence, the construction of good cyclic codes is of utmost importance. A generic class of polynomials called generator polynomials is used to construct the cyclic codes. Finding a generator polynomial necessitates factoring a base polynomial called monic polynomial. Unfortunately, factoring a polynomial is not always an easy task. Idempotent polynomials provide an alternative to get rid of this difficulty where factoring of a polynomial is not necessary. This paper presents different properties and classification of idempotent polynomials such as primitive idempotents and how idempotent polynomials outperform the generator polynomials in constructing good cyclic codes.
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