# Even code

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If the Hamming weight of all of a binary code's codewords is even

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A binary [linear code](/source/Linear_code) is called an **even code** if the [Hamming weight](/source/Hamming_weight) of each of its codewords is even. An even code should have a generator polynomial that includes the (*x*+1) minimal polynomial as a product. Furthermore, a binary code is called **doubly even** if the Hamming weight of all its codewords is [divisible by 4](/source/Divisible_by_4). An even code which is not doubly even is said to be strictly even.

Examples of doubly even codes are the extended binary [Hamming code](/source/Hamming_code) of block length 8 and the extended [binary Golay code](/source/Binary_Golay_code) of block length 24. These two codes are, in addition, [self-dual](/source/Self-dual_code).

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