A weight distribution bound for linear codes
Jean-Jacques Lévy · IEEE Transactions on Information Theory · 1968
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 thand. The weight distribution of the code is given by the set of allW(j), d \leq j \leq n, describing the number of code words having a weight of exactlyj. Exact weight distributions are known for only a handful of linear codes. This paper presents an explicit upper bound uponW(j)as a function ofn, d, andj. The bound has general applicability to all linear codes.