Codes and Designs

Abstract

We denote by V(n,q) the set of all n-tuples from a q-symbol alphabet F (i.e. V(n,q) = F ⁿ). If q is a prime power we take F = F _q and interpret V(n,q) as n-dimensional vector space over F _q any case we distinguish an element of F and denote it by 0. The elements of V(n,q) are called words (or vectors) and are denoted by underlined symbols. The word (0,0,…,0) is denoted by 0. The (Hamming) distance d(x,y) of two words x and y is defined by ${\rm{d}}(\underline {\rm{x}} ,\underline y ): = \left\{ {{\rm{i}}\left| 1 \right.} \right. \le {\rm{i}} \le {\rm{n,}}{{\rm{x}}_{\rm{i}}}\left. {{{\rm{y}}_{\rm{i}}}} \right\}$