By Scott A. Vanstone
Five. 2 earrings and beliefs 148 five. three beliefs and Cyclic Subspaces 152 five. four Generator Matrices and Parity-Check Matrices 159 five. five Encoding Cyclic Codest 163 five. 6 Syndromes and easy deciphering approaches 168 five. 7 Burst mistakes Correcting a hundred seventy five five. eight Finite Fields and Factoring xn-l over GF(q) 181 five. nine one other strategy for Factoring xn-l over GF(q)t 187 five. 10 routines 193 bankruptcy 6 BCH Codes and limits for Cyclic Codes 6. 1 creation 201 6. 2 BCH Codes and the BCH sure 205 6. three Bounds for Cyclic Codest 210 6. four deciphering BCH Codes 215 6. five Linearized Polynomials and discovering Roots of Polynomialst 224 6. 6 workouts 231 bankruptcy 7 errors Correction options and electronic Audio Recording 7. 1 advent 237 7. 2 Reed-Solomon Codes 237 7. three Channel Erasures 240 7. four BCH interpreting with Erasures 244 7. five Interleaving 250 7. 6 blunders Correction and electronic Audio Recording 256 7.
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Extra resources for An introduction to error correcting codes with applications
These result objects are revisited later in the chapter. The “Making Named Objects” section provides a look at listing the objects created as well as some rules for object names. Most often you will have sets of data to examine; these will comprise more complicated sets of numbers. Being able to create more complex data is covered in the next section. 30 ❘ CHAPTER 2 Starting Out: Becoming Familiar with R Reading and Getting Data into R So far you have looked at some simple math. More often you will have sets of data to examine (that is, samples) and will want to create more complex series of numbers to work on.
The window initially appears blank and you can click the Get List button to acquire the list from your selected source, which by default is the CRAN list of binary packages (those compiled and ready to go). Figure 1-23 Command Packages ❘ 19 Figure 1-24 The next task is to select the package(s) you require and click the Install Selected button. (You can select multiple items using Cmd+click, Shift+click, and so on). It is simplest to locate the new packages in the default location (at the system level), where they are then available for all users.
More often you will have sets of data to examine (that is, samples) and will want to create more complex series of numbers to work on. You cannot perform any analyses if you do not have any data so getting data into R is a very important task. This next section focuses on ways to create these complex samples and get data into R, where you are able to undertake further analyses. Using the combine Command for Making Data The simplest way to create a sample is to use the c() command. You can think of this as short for combine or concatenate, which is essentially what it does.