ABSTRACT
A binary code is linear if it is closed under addition. It is a basic fact from linear algebra that each linear code has a basis. Linear algebra applies to arbitrary fields. There is a general tendency to restrict attention to linear codes. One reason is that these are much easier to describe and to work with than codes in general. For a binary linear code, the minimum distance equals the minimum of the weights of nonzero codewords. Binary linear codes are particularly handy for block coding. In block coding the length of bitstrings is increased from k to n. That means that k/n of the bits sent through the channel represent pure information, whereas the rest is redundancy that we have cleverly introduced for the purposes of error correction.
