A
binary code
A binary code represents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, als ...
is called an even code if the
Hamming weight
The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a string o ...
of each of 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
In mathematics an even integer, that is, a number that is divisible by 2, is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly even if it is not. The former names are traditional ones, derived from ancient Gre ...
. 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
In computer science and telecommunication, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the s ...
of block length 8 and the extended binary
Golay code of block length 24. These two codes are, in addition,
self-dual.
{{crypto-stub
Coding theory
Parity (mathematics)