## Coding Theory

Let F=GF(p). A linear [n,k] code C over F is a
k-dimensional vector subspace of F^{n}. The elements of C are
called codewords and the weight wt(x) of a codeword x is the
number of non-zero coordinates in x. The minimum weight of C
is defined as min{wt(x): | 0 ≠ x in C}. An [n,k,d]
code is an [n,k] code with minimum weight d. A matrix whose
rows generate the code C is called a generator matrix of C.
The dual code of C is defined as {x in F^{n}
| xy ≡ 0 (mod p) for all y in C}. C
is self-dual if C is equal to its dual. We say that self-dual codes
with the largest minimum weight among self-dual codes of that
length are extremal.
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