Zero of a cyclic code
= Zero of a cyclic code
= Zeros of a cyclic code
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= Defining zero of a cyclic code
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= Defining zeros of a cyclic code
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A zero of a <cyclic code> is a <polynomial root> of its <generator polynomial>, taken in a <splitting field>. Every <codeword>, represented as a <polynomial>, vanishes there. For a <repeated-root cyclic code>, the <multiplicity of a root> must also be retained: ordinary evaluations alone need not determine the code.