ECE259A: Slides from Lectures, Fall 2021

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Algebraic Coding: Motivation and Introduction
Presented in class on September 29, 2021.


Hamming Metric and the Minimum Distance
Presented in class on September 29, 2021.


Singleton Bound and MDS Codes
Presented in class on September 29, 2021.


Linear Codes: Basic Properties
Presented in class on October 6, 2021.


Binary Symmetric Channel and Maximum Likelihood Decoding
Presented in class on October 6, 2021.


Cosets, Syndromes, and Standard Arrays
Presented in class on October 6 and October 13, 2021.


Bounds on Code Parameters
Presented in class on October 13, 2021.


Perfect Codes
Presented in class on October 13, 2021.


The Binary Golay Code
Presented in class on October 20, 2021.


Finite Fields: Basic Properties
Presented in class on October 20, 2021.


Finite Fields: Additive Structure
Presented in class on October 20, 2021.


Constructions of Extension Fields
Presented in class on October 27, 2021.


Double-Error-Correcting BCH Codes
Presented in class on October 27, 2021.


Finite Fields: Roots of Polynomials
Presented in class on October 27, 2021.


Finite Fields: Multiplicative Structure
Presented in class on October 27, 2021.


Finite Fields: Minimal Polynomials
Presented in class on November 3, 2021.

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