Coding theory MOC

Generalized Hamming weight

The Hamming $𝑡$ -weight, is a generalization of weight: #m/def/code Let $D \leq 𝕂 𝑛 𝑞$ be a $𝑡$ -dimensional subcode. Then

w t 𝑡 D = 𝑛 \sum 𝑖 = 1 [(\exists 𝑥 \in D) [𝑥 𝑖 \neq 0]]

where we have used an Iverson bracket. Clearly the case $𝑡 = 1$ reduces to the ordinary concept of weight.¹

Properties

MacWilliams theorem

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

2003. Generalized hamming weights and equivalences of codes ↩