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The [[generator polynomial]] of the BCH code is defined as the [[least common multiple]] {{math|''g''(''x'') {{=}} lcm(''m''<sub>1</sub>(''x''),…,''m''<sub>''d'' − 1</sub>(''x''))}}.
It can be seen that {{math|''g''(''x'')}} is a polynomial with coefficients in {{math|GF(''q'')}} and divides {{math|''x''<sup>''n''</sup> − 1}}.
Therefore, the [[polynomial code]] defined by {{math|''g''(''x'')}} is a cyclic code.
==== Example ====
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