Coding theory MOC

Generalized Hamming weight

The Hamming 𝑡-weight, is a generalization of ^weight: code Let D ≤𝕂𝑛𝑞 be a 𝑡-dimensional subcode. Then

wt𝑡⁡D=𝑛∑𝑖=1[(∃𝑥∈D)[𝑥𝑖≠0]]

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

Properties

• MacWilliams theorem

---

tidy | en | SemBr

Footnotes

1. 2003. Generalized hamming weights and equivalences of codes ↩