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Orthodoxy, however, sought to preserve itself in a vast Kalpa-sutra (ritual) literature with three parts: the Shrauta-sutra, based on shruti (revelation); the Grihya-sutra, based on smriti (tradition); and the Dharma-sutra, pertaining to rules of religious law whereas the philosophers tried to codify their doctrines in systematic form, leading to the rise of the philosophical sutras.
Since only the parity symbols are transmitted, the generator matrix is in systematic form: G = [ I n | P ], (3).
The binary LDPC code in systematic form is specified by its parity-check matrix H: mathbf{H} = left[mathbf{I}_{N-K}; mathbf{P}right], (4).
To perform Gauss-Jordan elimination on the k×n original generator matrix G to obtain the generator matrix G ⋆ in systematic form, in which the information bits coincide with v ⋆.
A real convolution code in systematic form [16] is used to compute parity values associated with the processing outputs as shown in Figure 2. Certain classes of errors occurring anywhere in the overall system including the parity generation and regeneration subsystems are easily detected.
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The Brazilian reporting system of adverse events started in 1998 in a systematic form as specified in the " Manual de Vigilância Epidemiológica dos Eventos Adversos Pós-Vacinação".
In most of the standards, such as long-term evolution (LTE) standard [27], the encoding is performed in a systematic form in order to facilitate the decoding process without degrading performances of the error correction.
The N bits of a codeword are represented in the systematic form, divided in information bits (IN) and parity-check bits (PN) given by the number of columns of A and B, respectively.
Legendre published his own researches in number theory and those of his predecessors in a systematic form under the title Théorie des nombres, 2 vol. (1830).
The main algorithms that create G from H consist in arranging H in an appropriate form that allows to develop G and construct it in a systematic form.
SHADD and its elements are specified in a systematic form and an illustration of its application on the architecture of a real system is also presented.
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