Potential Project Topics for Essential Coding Theory (MIT 6.440):

1. A Mathematical Theory of Communication (by Claude Shannon). Project unassigned.
   
   
2. Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Binary Codes (by Tao Jiang and Alexander Vardy).
   Improving the Gilbert-Varshamov bounds for q-ary codes (by Van Vu and Lei Wu). Project unassigned.
   
   
3. Long Nonbinary Codes Exceeding the Gilbert - Varshamov Bound for any Fixed Distance (by Sergey Yekhanin and Ilya Dumer). Project unassigned.
   
   
4. Generalized Alon-Boppana Theorems and Error-Correcting Codes (by Joel Friedman and Jean-Pierre Tillich).
   Linear programming bounds for codes via a covering argument (by Michael Navon and Alex Samorodnitsky). Project unassigned.
   
   
5. A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound (by A. Garcia and H. Stichtenoth). Project unassigned.
   
   
6. Combinatorial Bounds for List Decoding (by V. Guruswami, J. Hastad, M. Sudan and D. Zuckerman).
   Limits to list decodability of linear codes (by V. Guruswami). Project unassigned.


7. Subspace Polynomials and List Decoding of Reed-Solomon Codes (by E. Ben-Sasson, S. Kopparty and J. Radhakrishnan). Project unassigned.
   
   
8. Limits to List Decoding Reed-Solomon Codes (by V. Guruswami and A. Rudra). Project assigned (Sam E. & Adam H.).
   
   
9. Maximum-Likelihood Decoding of Reed-Solomon Codes is NP-hard (by V. Guruswami and A. Vardy). Project unassigned.
   
   
10. Hardness of approximating the closest vector problem with pre-processing (by Michael Alekhnovich, Subhash Khot, Guy Kindler, Nisheeth Vishnoi). Project unassigned.
    
    
11. Linear Diophantine Equations over Polynomials and Soft Decoding of Reed-Solomon Codes (by Michael Alekhnovich). Project assigned (Tana & Pasin).
    
    
12. Pseudorandom generators without the XOR lemma (by M. Sudan, L. Trevisan, and S. Vadhan). Project assigned (Sam W. & Shravas).
    
    
13. Extractors and Pseudorandom Generators (by L. Trevisan). Project assigned (George & Tim).
    
    
14. Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes (by Venkatesan Guruswami, Christopher Umans, and Salil Vadhan). Project unassigned.
    
    
15. When Hamming Meets Euclid: the Approximability of Geometric TSP and MST (by Luca Trevisan). Project assigned (Jon & Josh). Link broken - to be updated.
    
    
16. Towards 3-Query Locally Decodable Codes of Subexponential Length (by Sergey Yekhanin). 3-Query Locally Decodable Codes of Subexponential Length (Klim Efremenko). Project unassigned
    


17. Subspace Evasive Sets (by Zeev Dvir and Shachar Lovett). Project assigned (Efrat & Chiheon).
    


18. How to construct Polar Codes. (by Ido Tal and Alexander Vardy). Project unassigned.
    


19. Coding for Errors and Erasures in Random Network Coding (by Ralf Koetter and Frank Kschischang). Project assigned (Mina & Ali).
    


20. Quantum algebraic geometry codes (by Chiu Fan Lee). Project assigned (Alan & Matt).
    


21. List-decoding Reed Muller Codes (by Parikshit Gopalan, Adam Klivans and David Zuckerman). Project assigned (Mohammad & Badih).
    


22. Coding for interactive communication (by Zvika Brakerski and Yael Kalai). Project assigned (Mohsen & Zonghao).