Coding theory MOC

Weight enumerator

Let $C \subseteq 𝑆 𝑛 𝑞$ be a $𝑞$ -ary code of length $𝑛$ . Then the weight enumerator is of $C$ is defined by¹² #m/def/code

w t (C; 𝑞) = \sum 𝑐 \in C 𝑞 w t 𝑐 \in ℤ [𝑞]

Properties

MacWilliams identities relate the weight enumerator of a code and its dual.

#state/tidy | #lang/en | #SemBr

1988. Vertex operator algebras and the Monster, §10.1, p. 300 ↩
1999. Introduction to coding theory, §3.5, pp. 40–41 ↩