If C1 has only even weight codewords, what is the relationship between (1+x) and g1(x)?

In coding theory, the relationship between a code \( C_1 \) consisting of only even weight codewords and the polynomial \( g_1(x) \) can be explained using the concept of weight enumerators and generating functions.

The weight enumerator of a code \( C \) counts the number of codewords of each possible weight in the code. For a linear code represented by its ________ ___ __________ _________ ______ ______ _____ ___ __________.
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