Besides the generating polynomial, there are many other polynomials that can be used to generate a cyclic code. One such another vary specific polynomial called an idempotent generator, can also be used to generate a cyclic code. As the ring Rn is semi-simple therefore each ideal in Rn contains a unique idempotent which also generates the ideal. This idempotent is called the generating idempotent of the corresponding cyclic code. The idempotent generating the minimal ideal (minimal code) in Rn is called a Primitive idempotent

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References

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