6.895 | Fall 2004 | Graduate
Essential Coding Theory

Lecture Notes

This section contains a set of lecture notes and scribe notes for each lecture. Scribe notes are latex transcriptions by students as part of class work. Scribe notes are used with permission of the students named.

lec # TOPICS Scribe notes

Lecture 1 (PDF)


Hamming Space, Distance, Code


Piotr Mitros (PDF)

Lecture 2 (PDF)

Shannon’s Theory of Information

The Coding Theorem

Its Converse

Joungkeun Lim (PDF)

Lecture 3 (PDF)

Shannon Theory vs. Hamming Theory

Our Goals


Linear Codes

Adi Akavia (PDF)

Lecture 4 (PDF)

Asymptotically Good Codes

Projection and Volume Bound

Random Codes

Victor Chen (PDF)

Lecture 5 (PDF)

Algebraic Codes: Reed-Solomon, Reed-Muller, Hadamard

Plotkin Bound

Swastik Kopparty (PDF)
6 Decoding Reed-Solomon Codes - The Welch-Berlekamp Algorithm Kyomin Jung (PDF)

Abstracting the RS Decoding Algorithm

Beyond Unique Decoding

Kunal Agrawal (PDF)
8 List Decoding of Reed-Solomon Codes Anindya Patthak (PDF)

Concatenated Codes and Decoding

Justesen Codes

Jesse Kamp (PDF)
10 Achieving Shannon Capacity in Polytime with Concatenated Codes Elena Grigorescu (PDF)
11 List Decoding versus Rate versus Distance Anastasios Sidiropoulos (PDF)
12 The Gap between Constructive and Existential Results in Coding Theory Kevin Matulef (PDF)
13 Algebraic Geometry Codes Alexey Spiridonov (PDF)
14 Linear-time Decodable Codes Vinod Vaikuntanathan (PDF)
15 Linear-time Encodable and Decodable Codes Reina Riemann (PDF)

Spielman Codes and Decoding

Correcting Random Error in Linear Time, Expander Codes (Type II)

Abhinav Kumar (PDF)
17 Expander Codes - the ABNNR Construction Venkat Chandar (PDF)
18 Computation and Randomness: Pseudo-randomness, Limited Independence, Small-bias Spaces Kyomin Jung (PDF)
19 Extraction of Randomness, Min-entropy, Statistical Difference, Extractors and Codes Anup Rao (PDF)
20 Trevisan’s Extractor  
21 Ta-Shma-Zuckerman-Safra Extractor, Guruswami-codes Paul Valiant (PDF)
22 Ta-Shma-Zuckerman-Safra Extractor (cont.) Swastik Kopparty (PDF)
23 Expanders, Eigenvalues and the Zig-Zag Product Victor Chen (PDF)
24 TBA  
25 TBA  
Course Info
As Taught In
Fall 2004