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The inner code could be a convolutional one or a trellis code modulation The mostly used outer code is in general a Reed-Solomon code based on a finite field, or a Galois field For an introduction to the finite field calculation, and to the BCH and Reed-Solomon codes, see [Ref 3-9], [Ref 3-17 to 20] for a in-depth understanding The BCH codes are a class of block codes capable of correcting multiple symbol errors, named after their discoverers: Bose-Chaudhuri-Hocquenghem These are cyclic codes in a symbol field, with their roots in another field called localization field For example, the binary BCH codes of length 2m-1 are constructed over their symbol field GF(2), but for their algebraic decoding, operations are performed in their localization field GF(2m) When these two fields are the same, the Reed-Solomon codes result In general, the usual description of BCH codes is in cyclic code language, i.

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e, by using generating polynomials To demonstrate their error correction capability, however, the block code language is more useful and matrix and determinant properties are used, see [Ref 3-9] The additional defining parameters of a BCH code, of length n and dimension k, designed to correct errors, are the symbol field KS and its localization field KL The minimum Hamming distance is not given explicitly The BCH bound holds always d 2t+1, d being called the true distance From the defining parameter t of the BCH codes, d*=2t+1 is called the designed distance The Reed-Solomon codes are a special class of the BCH codes defined over the finite field GF(qm), q a prime Here q is supposed to equal 2 to simplify the explanation Its dimension is now given exactly as k=n 2t, and the Singleton bound holds with equality: d=n k+1=2t+1.

The designed distance is the true distance for the Reed-Solomon codes This is an important property of these codes, because it has been shown that for given length and dimension, d=n k+1 is the largest distance that can be obtained for any block code The codes that meet the Singleton bound by equality are known as MDS (maximum distance separable) codes The Reed-Solomon codes are MDS codes and are the best codes for concatenated coding systems Usually the Reed-Solomon codes are constructed over GF(2m) In this case, since a symbol is equivalent to m bits, correcting t symbol errors implies that at most mt bits can be corrected This shows the burst-error correction capability of the Reed-Solomon codes..

the product was quickly eroding. Kurt Gentry, one of our data analysts, began gathering information about the weight-loss pill from various sources. Several Local Market detectives began reporting incidents of theft, and several stores claimed they were ordering more units than they were selling. When Kurt presented this information to me, I immediately assigned Investigator Andy Peters to the case.

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Like most data analysis exercises, principal component analysis starts with a data table comprising a series of observations. Each observation is characterized by a number of variables. The rst step in generating the principal components is to construct either a correlation matrix or a covariance matrix. If a covariance matrix is used, the original data may need to be normalized to ensure all variables are on a consistent range. If a correlation matrix is used, this matrix is generated by computing a correlation coef cient (r) for each pair of variables (see Section 3.2.5). For example, Fig. 4.12 shows a correlation matrix formed from a series of 13 variables: age ( year), weight (lbs), and so on. The variable age ( years) is correlated with each other variable, shown in the rst row and rst column. For example, the correlation coef cient between age ( years) and weight (lbs) is 0.0125.

for(ivar = 0; ivar <= 10; ivar++)

Uniform technical Gathering (SNG)

<complexType name= ProductType > <element name= Name type= string /> <element name= Description type= string minOccurs= 0 /> <element name= Price > <complexType content= decimal > <attribute name= currency type= string /> </complexType> </element> </complexType>

(A.32)