Instructor: Swastik
Kopparty (swastik.kopparty@gmail.com)

Class Time and Place: Thursdays, 12
noon – 3pm, in Hill 009

Office Hours: Wednesday 10:00-11:00
(Hill 432)

Prerequisites: basics of
algorithms, complexity theory, probability, graph theory, linear algebra,
mathematical maturity.

References: various online sources,
scribe notes.

__Syllabus__

This course will be an introduction
to the theoretical aspects of error-correcting codes, with many applications to
complexity theory.

Students will take turns scribing
the lectures, and the notes will be put up here. There will be 2-3 problem
sets.

Latex files for scribes: definitions, main file,
guidelines.

__Homework__

·
Homework
1 (due Feb 4, but some parts are due earlier if you need permission to
register)

·
Homework
2 (due March 24)

__Lecture Schedule__

·
January 21: the
main problems of coding theory, basic bounds on codes (notes)

·
January 28: more bounds
on codes, Shannon’s theorem for random errors (notes)

·
February 4: codes
based on polynomials (notes)

·
February 11:
concatenated codes (notes)

·
February 18: BCH
codes (notes)

·
**February 25: class cancelled (makeup class
to be scheduled)**

·
March 3: expander
codes, expander distance amplification (notes)

·
**March 10: class cancelled (makeup class to
be scheduled)**

·
**March 17: SPRING BREAK**

·
March 24: expander
distance amplification, list-decoding (notes)

·
March 31:
list-decoding, list-decoding Reed-Solomon codes (notes)

·
April 7:
list-decoding concatenated codes, list-decoding Folded Reed-Solomon codes (notes)

·
April 14:
list-decoding Folded Reed-Solomon codes, locally decodable codes based on
polynomials (notes)

·
**Tuesday April 19, 12 noon – 3pm: **(NOTE UNUSUAL DAY) matching-vector codes (notes)

·
April 21: multiplicity
codes (notes)

·
**Tuesday April 26, 12 noon – 3pm: **(NOTE UNUSUAL DAY)** **worst-case to average-case reductions, Fourier-based
bounds for codes (notes)

·
April 28: codes
better than random (notes)