---
tag: HZ5CX9Y5W9
kind: concept
name: Johnson scheme
sources:
  - wikipedia: en:22649423@r1169848354
    locator: Johnson scheme
    note: adopted
    mention: wikipedia://en/22649423
    sections: [Summary]
same_as:
  wikidata: Q6268497
  wikipedia: Johnson scheme
inventory: [DV1ASN9KAY]
---

## Summary

In mathematics, the **Johnson scheme**, named after Selmer M. Johnson, is also known as the triangular association scheme. It consists of the set of all binary vectors *X* of length *ℓ* and weight *n*, such that $v=\left|X\right|=\binom{\ell}{n}$. Two vectors *x*, *y* ∈ *X* are called *i*th associates if dist(*x*, *y*) = 2*i* for *i* = 0, 1, ..., *n*. The eigenvalues are given by