Dual Code

In coding theory, the dual code of a linear code

is the linear code defined by

where

is a scalar product. In linear algebra terms, the dual code is the annihilator of C with respect to the bilinear form <,>. The dimension of C and its dual always add up to the length n:

A generator matrix for the dual code is a parity-check matrix for the original code and vice versa. The dual of the dual code is always the original code.

Read more about Dual CodeSelf-dual Codes

Other articles related to "dual code, dual, codes, dual codes":

Dual Code - Self-dual Codes
... A self-dual code is one which is its own dual ... If a self-dual code is such that each codeword's weight is a multiple of some constant, then it is of one of the following four types Type I codes are binary self-dual codes which are ... Type I codes are always even (every codeword has even Hamming weight) ...

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