Let be a linear code of block length over the finite field . Then the set
This definition is reminiscent of orthogonal complements of http://planetmath.org/node/5398finite dimensional vector spaces over the real or complex numbers. Indeed, is also a linear code and it is true that if is the http://planetmath.org/node/5398dimension of , then the of is . It is, however, not necessarily true that . For example, if is the binary code of block length http://planetmath.org/node/806spanned by the codeword then , that is, . In fact, equals in this case. In general, if , is called self-dual. Furthermore is called self-orthogonal if .
Famous examples of self-dual codes are the extended binary Hamming code of block length and the extended binary Golay code of block length .
|Date of creation||2013-03-22 15:13:29|
|Last modified on||2013-03-22 15:13:29|
|Last modified by||GrafZahl (9234)|