A binary code is called an even code if the Hamming weight of all its codewords is even. 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. The term binary code can mean several different things: There are a variety of different methods of coding numbers or symbols into strings of bits, including fixed-length binary numbers, prefix codes such as Huffman codes, and other coding techniques including arithmetic coding. ... The Hamming weight of a string of bits is the number of 1s in it. ...

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. In mathematics, duality has numerous meanings. ...

This article incorporates material from even code on PlanetMath, which is licensed under the GFDL. PlanetMath is a free, collaborative, online mathematics encyclopedia. ...