Error-correcting codes

 

tl;dr: Too many FRI conjectures that need to be understood, so here we are…

$ \def\L{\mathcal{L}} \def\RS{\mathsf{RS}} \def\CRS{\mathsf{CRS}} $

Glossary

Basics

  • code
  • linear code
    • generator matrix
    • Reed-Solomon (RS)
      • $\RS[\F,\L, m]$
    • Reed-Muller
  • codeword
  • rate
  • distance of a codeword from the code
  • distance of a code

Advanced

  • proximity
  • list decoding
  • $(\delta,\varepsilon)$-correlated agreement for $\RS[\F,\L, m]$
  • $(\delta, \varepsilon)$ mutual correlated agreement for $\RS[\F,\L, m]$
  • constrained Reed Solomon codes $\CRS[\F,\L,m, \hat{w}, \sigma]$
  • unique decoding regime
  • capacity bound
  • Johnson bound
  • ?

References

For cited works, see below 👇👇