In coding theory, the weight enumerator polynomial of a binary linear code specifies the number of words of each possible Hamming weight.
The weight distribution is the sequence of numbers giving the number of codewords c in C having weight t as t ranges from 0 to n. The weight enumerator is the bivariate polynomial Denote the dual code of
The distance distribution or inner distribution of a code C of size M and length n is the sequence of numbers where i ranges from 0 to n. The distance enumerator polynomial is and when C is linear this is equal to the weight enumerator.
The outer distribution of C is the 2n-by-n+1 matrix B with rows indexed by elements of GF(2)n and columns indexed by integers 0...n, and entries The sum of the rows of B is M times the inner distribution vector (A0,...,An).
A code C is regular if the rows of B corresponding to the codewords of C are all equal.