Enumerator Polynomial - Distance Enumerator

Distance Enumerator

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.

Read more about this topic:  Enumerator Polynomial

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