Combinatorics MOC

𝑑-design

A 𝑑 βˆ’(𝑛,π‘˜,πœ†) design (𝑆,ℬ) consists of a set 𝑆 of 𝑛 points and a set ℬ βŠ†P(𝑆) of distinguished subsets of π‘˜ points, called blocks, such that for every 𝑇 βŠ†π‘† with |𝑇| =𝑑, there is exactly are exactly πœ† blocks 𝐡 βˆˆβ„¬ such that 𝑇 βŠ†π΅.1

  • A 𝑑 βˆ’(𝑛,π‘˜,1) design is a S⁑(𝑑,π‘˜,𝑛) Steiner system

develop | en | SemBr

Footnotes

  1. 1999. Introduction to coding theory, Β§1.3, p. 17 ↩

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