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 assigned (Ankur + Aleksander).
   
   
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 assigned (Minji + Daniel + Shirley).
   
   
7. Subspace Polynomials and List Decoding of Reed-Solomon Codes (by E. Ben-Sasson, S. Kopparty and J. Radhakrishnan). Project assigned (Minji + Daniel + Shirley).
   
   
8. Limits to List Decoding Reed-Solomon Codes (by V. Guruswami and A. Rudra). Project unassigned.
   
   
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 half-assigned (Huy + ?).
    
    
12. Pseudorandom generators without the XOR lemma (by M. Sudan, L. Trevisan, and S. Vadhan). Project assigned (Shira + Yinmeng).
    
    
13. Extractors and Pseudorandom Generators (by L. Trevisan). Project assigned (Shubhangi + Jelani).
    
    
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 unassigned.
    
    
16. Towards 3-Query Locally Decodable Codes of Subexponential Length (by Sergey Yekhanin). Project unassigned.