Trance-0/NoteNextra-origin
1
0
Fork 0
Code Issues Pull Requests Actions 1 Packages Projects Releases Wiki Activity

Update CSE5313_L6.md

Browse Source
This commit is contained in:
Trance-0
2025-10-28 10:14:51 -05:00
parent 6acd8adf32
commit e4490f6fa2
1 changed files with 5 additions and 4 deletions
Download Patch File Download Diff File Expand all files Collapse all files

9
content/CSE5313/CSE5313_L6.md
View File

@@ -233,9 +233,10 @@ Compare with exhaustive search: Time: $O(|F|^n)$.
#### Syndrome decoding - Intuition
Given 𝒚′, we identify the set 𝐶 + 𝒆 to which 𝒚′ belongs by computing the syndrome.
• We identify 𝒆 as the coset leader (leftmost entry) of the row 𝐶 + 𝒆.
• We output the codeword in 𝐶 which is closest (𝒄3) by subtracting 𝒆 from 𝒚′.
Given $y'$, we identify the set $\mathcal{C} + e$ to which $y'$ belongs by computing the syndrome.
- We identify $e$ as the coset leader (leftmost entry) of the row $\mathcal{C} + e$.
- We output the codeword in $\mathcal{C}$ which is closest ($c'$) by subtracting $e$ from $y'$.
#### Syndrome decoding - Formal
@@ -243,4 +244,4 @@ Given $y'\in \mathbb{F}^n$, we identify the set $\mathcal{C}+e$ to which $y'$ be
We identify $e$ as the coset leader (leftmost entry) of the row $\mathcal{C}+e$.
We output the codeword in $\mathcal{C}$ which is closest ($c_3$) by subtracting $e$ from $y'$.
We output the codeword in $\mathcal{C}$ which is closest (example $c_3$) by subtracting $e$ from $y'$.