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===Factor error locator polynomial=== Now that you have the <math>\Lambda(x)</math> polynomial, its roots can be found in the form <math>\Lambda(x) = \left(\alpha^{i_1} x - 1\right)\left(\alpha^{i_2} x - 1\right) \cdots \left(\alpha^{i_v} x - 1\right)</math> by brute force for example using the [[Chien search]] algorithm. The exponential powers of the primitive element <math>\alpha</math> will yield the positions where errors occur in the received word; hence the name 'error locator' polynomial. The zeros of Ξ(''x'') are ''Ξ±''<sup>β''i''<sub>1</sub></sup>, β¦, ''Ξ±''<sup>β''i''<sub>''v''</sub></sup>.
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