Section Daily Prep 3
Today we will review the connection between minimum distance and error-correcting capability for codes, and introduce a highly useful class of codes called linear codes through the example of the Hamming code.
Subsection Learning Objectives
Subsubsection Basic Learning Objectives
Before our class meeting, you should use the resources below to be able to learn the following. You should be reasonably fluent with these; we’ll answer some questions on them in class but not reteach them in detail.
Subsubsection Advanced Learning Objectives
During our class meeting, we will work on learning the following. Fluency with these is not expected or required before class.
-
State the definition and give examples of: finite field, vector space.
-
Determine the minimum distance of the \((7,4)\) Hamming code.
-
Explain and apply Proposition 1.5.4 (relation between minimum distance and Hamming weight for binary linear codes).
Subsection Resources for Learning
Use these resources to prepare for class and answer the questions below.
-
Guruswami, Rudra, & Sudan, Sections, 1.4-5, 2.1, pp. 12-18, 31-33
-
Roth, Section 2.1, pp. 26-27
Exercises Exercises
2.
3.
4.
5.
In your own words, what is a binary linear code?
6.
T/F: The parity code \(C_{\oplus}\) formed by appending a parity check bit to a 4 bit message is a binary linear code.
7.
What questions do you have about the material for today?
