Bounds on codes

Abstract

We now return to the problem of finding bounds on codes and the study of the function α(δ) defined in (2.5). We need a few definitions and lemmas. If we consider the set of words in IF ⁿ _q that have distance at most d to a fixed word, then the cardinality of this set is

$$ {V_q}(n,d): = \sum\limits_{{i = 0}}^d {\left( {_i^n} \right){{\left( {q - 1} \right)}^i}} $$

((6.1))