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Contents Embed Dark Mode Prev Up Next \(\require{mathtools} \setcounter{MaxMatrixCols}{15}
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Section Daily Prep 15
Today we’ll discuss the connection between the polynomial and matrix/vector points of view for GRS and RS codes, and begin to discuss encoding for this class of codes. We’ll also discuss how to write a GRS/RS code as a code over the prime field (or binary field) and what implications, good and bad, that has for their use.
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
State and give examples of the definition of conventional Reed-Solomon (RS) codes, roots of an RS code, generator polynomial.
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
Use the generator polynomial of an RS code to do encoding.
Write a GRS/RS code as a code over
\(\F_p\) or over
\(\F_2\text{.}\)
Subsection Resources for Learning
Use these resources to prepare for class and answer the questions below.
Roth, Sections 5.1-3, pp. 148-154
Subsection Important Terms
