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Convolutional codes are often characterized by the base code rate and the depth (or memory) of the encoder . The base code rate is typically given as , where n is the raw input data rate and k is the data rate of output channel encoded stream. n is less than k because channel coding inserts redundancy in the input bits.
In linear algebra terms, the dual code is the annihilator of C with respect to the bilinear form . The dimension of C and its dual always add up to the length n : A generator matrix for the dual code is the parity-check matrix for the original code and vice versa. The dual of the dual code is always the original code.
A linear code of length n and dimension k is a linear subspace C with dimension k of the vector space where is the finite field with q elements. Such a code is called a q -ary code. If q = 2 or q = 3, the code is described as a binary code, or a ternary code respectively. The vectors in C are called codewords.
Its generator polynomial as a cyclic code is given by. where is the set of quadratic residues of in the set and is a primitive th root of unity in some finite extension field of . The condition that is a quadratic residue of ensures that the coefficients of lie in . The dimension of the code is . Replacing by another primitive -th root of unity ...
The QR code system was invented in 1994, at the Denso Wave automotive products company, in Japan. The initial alternating-square design presented by the team of researchers, headed by Masahiro Hara, was influenced by the black counters and the white counters played on a Go board; the pattern of position detection was found and determined by applying the least-used ratio (1:1:3:1:1) in black ...
In electricity generation, a generator [1] is a device that converts motion-based power ( potential and kinetic energy) or fuel-based power ( chemical energy) into electric power for use in an external circuit. Sources of mechanical energy include steam turbines, gas turbines, water turbines, internal combustion engines, wind turbines and even ...