A weight distribution bound for linear codes

A linear code of block length n possessing minimum weight d has one code word of weight zero, and no other code words of weight less than
d
. The weight distribution of the code is given by the set of all
W(j), d \leq j \leq n
, describing the number of code words having a weight of exactly
j
. Exact weight distributions are known for only a handful of linear codes. This paper presents an explicit upper bound upon
W(j)
as a function of
n, d
, and
j
. The bound has general applicability to all linear codes.