Even code: Difference between revisions

Revision as of 15:21, 11 April 2006

Revision as of 07:19, 4 December 2006

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A [[binary code]] is called an '''even code''' if the [[Hamming weight]] of all its codewords is even. An Even code should have a generator polynomial that include (1+x) 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. 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 of [[block length]] 8 and the [[extended binary Golay code]] of block length 24. These two codes are, in addition, [[self-dual]].