Defintions
A binary code is subset of n dimensional binary space. The standard
inner-product is given by
[x,y]= x_1 y_1 + x_2 y_2 + ... + x_n y_n.
The orthogonal to the code C* = { v | [v,x] = 0 for all x in C}.
If C is contained in C* then C is self-orthogonal and if C=C* then C is
self-dual. The Hamming weight of a vector is the number of non-zero
entries and the minimum Hamming weight of a code is the smallest
non-zero Hamming weights of vectors in C. An [n,k,d] code has length n,
dimension k and minimum Hamming weight weight d.
For a complete description of self-dual codes see Chapter 19 of
MacWillams and
Sloane's book "The Theory of Error-Correcting Codes".
To learn about the connection between self-dual codes and unimodular lattices, see
the excellent book, "Sphere Packings, Lattices and Groups" by J.H. Conway
and
N.J.A. Sloane and the references therein.
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