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Section Daily Prep 14
Today we’ll see how to define generalized Reed-Solomon codes, discuss the connection between the polynomial and matrix/vector points of view for these codes, and begin to discuss encoding for this class of codes.
Subsection Learning Objectives
Subsubsection Basic Learning Objectives
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.
State and give examples of the definition of generalized Reed-Solomon (GRS) codes, code locators, column multipliers, primitive GRS code, normalized GRS code, narrow-sense GRS code, (singly) extended GRS code
Subsubsection Advanced Learning Objectives
Objectives
During our class meeting, we will work on learning the following. Fluency with these is not expected or required before class.
State and explain the proposition that the dual of a GRS code is a GRS code with the same code locators.
Explain the correspondence between the generator/parity check definition of GRS codes and the polynomial interpretation of GRS codes
State and give examples of the definition of conventional Reed-Solomon (RS) codes, roots of an RS code, generator polynomial.
Use the generator polynomial of an RS code to do encoding.
Subsection Resources for Learning
Use these resources to prepare for class and answer the questions below.
Roth, Sections 5.1-5.2, pp. 148-152
Subsection Important Terms
