Coding Theory

Let F=GF(p). A linear [n,k] code C over F is a k-dimensional vector subspace of Fn. 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 Fn | 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. Also interesting are the following links: