EECS 298, Proof that j is a root of Q1(x) for Sudans algorithm
with l = 1.
We know that Q(j , yj ) = 0 by the 3rd constraint of Q(x, z). We also know that (x) =
Q(x, u(x) = 0 is the zero polynomial. Thus, for all j J being an error location,
(j ) = Q(j ,

EECS 298
Topics in Coding Theory
UCI
Fall 2016
Homework #3
Due Thursday, Oct 13, 2016, in class
Recommended reading: Chapters 3.1, 3.4 of Channel codes: classical and
modern by Ryan and Lin.
1
Hamming Code, Repetition Code, and Single-Parity Code
Consider

EECS 298
Topics in Coding Theory
UCI
Fall 2016
Homework #1
Due Thur, Sep 29, 2016, in class
1
Hamming Code
Consider the (n = 7, k = 4) Hamming Code defined in class, shown in Figure 1.
(1) If the received word is r = (u0 , u1 , u2 , u3 , p0 , p1 , p2 ) =

EECS 298
Topics in Coding Theory
UCI
Fall 2016
Homework #4
Due Thursday, Oct 27, 2016, in class
Reading: Read chapters 4.1, 4.2, 4.3, 4.5 of Roth, introduction to coding theory.
Fact you can use for the homework:
Lemma 1. If X1 , X2 , . . . , Xm are iid u

EECS 298
Topics in Coding Theory
UCI
Fall 2016
Homework #2
Due Thursday, Oct 6, 2016, in class
1
ML Rule for q-ary Symmetric Channel
Consider q-ary symmetric channel. Prove that the maximum-likelihood rule becomes minimizing the Hamming distance:
min dH (

EECS 298
Topics in Coding Theory
UCI
Fall 2016
Project: Reed Solomon Codes
Due Thursday, Oct 20, 2016, in class.
Reading: Find Linear Bivariate Factors. Read chapter 9.7 from Roth, introduction
to coding theory, pages 284 to 289 (uploaded).
Goal. In this