This commit is contained in:
Trance-0
2025-11-20 13:03:44 -06:00
parent d90faea29b
commit 970ee8fa5a
7 changed files with 475 additions and 4 deletions

View File

@@ -160,14 +160,14 @@ Can we trade the recovery threshold $K$ for a smaller $s$?
#### Construction of Short-Dot codes
Choose a super-regular matrix $B\in \mathbb{F}^{P\time K}$, where $P$ is the number of worker nodes.
Choose a super-regular matrix $B\in \mathbb{F}^{P\times K}$, where $P$ is the number of worker nodes.
- A matrix is supper-regular if every square submatrix is invertible.
- Lagrange/Cauchy matrix is super-regular (next lecture).
Create matrix $\tilde{A}$ by stacking some $Z\in \mathbb{F}^{(K-M)\times N}$ below matrix $A$.
Let $F=B\dot \tilde{A}\in \mathbb{F}^{P\times N}$.
Let $F=B\cdot \tilde{A}\in \mathbb{F}^{P\times N}$.
**Short-Dot**: create matrix $F\in \mathbb{F}^{P\times N}$ such that: