Coding theory MOC

Weight enumerator

Let C ⊆𝑆𝑛𝑞 be a 𝑞-ary code of length 𝑛. Then the weight enumerator is of C is defined by¹² code

wt⁡(C;𝑞)=∑𝑐∈C𝑞wt⁡𝑐∈ℤ[𝑞]

Properties

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

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Footnotes

1. 1988. Vertex operator algebras and the Monster, §10.1, p. 300 ↩

2. 1999. Introduction to coding theory, §3.5, pp. 40–41 ↩