Massachusetts Institute of Technology · Electrical Engineering and Computer Science

6.S953: Topics in Error-Correcting Codes for Computer Science

Fall 2026 · Graduate · 12 units

This topics course in error-correcting codes begins with the fundamentals, progresses to the research frontier, and explores recent developments in the field.

Professor
Yael T. Kalai
tauman@mit.edu
TA / co-lecturer
Rohan Goyal
rohan_g@mit.edu
Time
Mon & Wed
11:00–12:30
Location
36-156

Overview

This topics course in error-correcting codes begins with the fundamentals, progresses to the research frontier, and explores recent developments in the field. Principal areas include existence results and limitations for error-correcting codes, constructions and algorithms, interactive coding, subspace designs, and applications in computer science.

Prerequisites

6.1200, 6.1210, and 18.06.

Syllabus

The course is organized into the following modules. Lecture-level topics, notes, and references will be added to the schedule as the course develops. The midterm is scheduled for November 2, and the final two class meetings are reserved for project presentations.

  1. Foundations: Possibilities and limitations; Chapters 1–8 of GRS
  2. Interactive coding theory: Limitations of and improvements to error correction through interaction and feedback
  3. Code constructions: Algebraic and combinatorial techniques; Chapters 9–11 of GRS and more recent developments
  4. Subspace designs and LCL properties: Constructions of subspace-design codes, combinatorial techniques for list decoding, and equivalences among LCL properties
  5. Algorithms: List-decoding algorithms for Reed-Solomon and expander-based codes
  6. Applications: A range of applications across theoretical computer science

Logistics

Level and units

Graduate · 12 units

Prerequisites

6.1200, 6.1210, and 18.06

Requirement

AAGS in Theoretical Computer Science

Schedule

Classes meet Mondays and Wednesdays from 11:00–12:30. Calendar exceptions are noted below.

Course lectures, dates, lecturers, topics, notes, and references
Course no. & dateLecturerTopicNotes & references
01Foundations
Lecture 01Yael KalaiIntroduction and basicsLecture 1 notes
Chapter 1 (GRS)
Lecture 02Rohan GoyalLinear codes and q-ary entropyChapters 2 and 3 GRS
Lecture 03Rohan GoyalGV and Singleton bounds; Reed-Solomon and MDS codesChapters 4 and 5 GRS
Lecture 04Rohan GoyalList-decoding bounds: capacity, Johnson, and generalized SingletonChapters 6–8 GRS
02Interactive coding theory
Lecture 05Yael KalaiThe interactive and feedback models
Lecture 06Yael Kalai
Lecture 07Yael Kalai
Lecture 08Yael Kalai
03Code constructions
Lecture 09Guest: Tim HsiehConcatenated codes and expanders
No classIndigenous Peoples' Day · Institute holiday
Lecture 10Rohan GoyalExpander codesMonday schedule of classes
Lecture 11Rohan GoyalPolynomial Codes
04Subspace designs and LCL properties
Lecture 12
Lecture 13
Lecture 14
Lecture 15
MidtermMidterm
05Algorithms
Lecture 16
Lecture 17
No classVeterans Day · Institute holiday
Lecture 18
Lecture 19
06Applications
Lecture 20
Lecture 21
Lecture 22
Lecture 23
Project presentationsPresentations
Project presentationsPresentations · Last course meeting

References

[GRS]

Venkatesan Guruswami, Atri Rudra, and Madhu Sudan, Essential Coding Theory, draft book.

[Sud23]

Madhu Sudan, Essential Coding Theory, course materials.

[Har24]

Prahladh Harsha, CSS.318.1: Coding Theory, TIFR, 2024.

[Woo25]

Mary Wootters, CS250/EE387: Error-Correcting Codes, Stanford University, Winter 2025. Lecture videos.

[Gur22]

Venkatesan Guruswami, CS 294-226: Advances in Error-Correcting Codes, UC Berkeley, Fall 2022.

[Kop22]

Swastik Kopparty, Topics in Error Correcting Codes, University of Toronto, Fall 2022.

Policies

Evaluation

The grade will be based on the following three components:

  • Course project — 50%. See the project details and timeline below.
  • In-class midterm — 20%.
  • Problem sets — 30%. See the problem-set details below.

Project

The project is completed in groups of two or three and may take one of two forms: research or reading.

Candidate projects for both forms will be added soon. You may also propose a topic that aligns with the course, subject to approval by the professor or TA. You may schedule a meeting with Rohan to discuss possible projects and ideas.

Project timeline:

  • October 2 at 6:00 PM — Topic and group selection (5%).
  • October 16 at 6:00 PM — One-page project proposal and plan (10%).
  • November 13 at 6:00 PM — One-page progress report (10%).
  • December 7 and 9 — Project presentations (15%).
  • December 11 — Eight- to ten-page project report or paper (10%).

Problem sets

There will be four problem sets, and the final grade will be based on your three highest scores. Each problem set will contain four to six problems, of which you are expected to solve at least three. You will then schedule a 15-minute meeting with the TA to present your solutions and answer questions about the three problems you chose.

Collaboration

Students may collaborate with classmates and use AI models to discuss course material. We strongly recommend limiting AI use to supporting understanding rather than solving problems. Students are responsible for all content in their projects, presentations, and submitted work.