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In standard coding theory notation for block codes, the Hadamard code is a [,,]-code, that is, it is a linear code over a binary alphabet, has block length, message length (or dimension) , and minimum distance /. The block length is very large compared to the message length, but on the other hand, errors can be corrected even in extremely noisy ...
Hadamard code could be constructed column by column : the column is the bits of the binary representation of integer , as shown in the following example. Hadamard code has minimum distance 2 r − 1 {\displaystyle 2^{r-1}} and therefore can correct 2 r − 2 − 1 {\displaystyle 2^{r-2}-1} errors.
Performance of CIRC: [7] CIRC conceals long bust errors by simple linear interpolation. 2.5 mm of track length (4000 bits) is the maximum completely correctable burst length. 7.7 mm track length (12,300 bits) is the maximum burst length that can be interpolated.
A convolutional code that is terminated is also a 'block code' in that it encodes a block of input data, but the block size of a convolutional code is generally arbitrary, while block codes have a fixed size dictated by their algebraic characteristics. Types of termination for convolutional codes include "tail-biting" and "bit-flushing".
The second meaning of "aggregation problem" is the theoretical difficulty in using and treating laws and theorems that include aggregate variables. A typical example is the aggregate production function. [2] Another famous problem is Sonnenschein-Mantel-Debreu theorem. Most of macroeconomic statements comprise this problem.
Given a prime number q and prime power q m with positive integers m and d such that d ≤ q m − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q m − 1 and distance at least d is constructed by the following method. Let α be a primitive element of GF(q m).
Kraft's inequality limits the lengths of codewords in a prefix code: if one takes an exponential of the length of each valid codeword, the resulting set of values must look like a probability mass function, that is, it must have total measure less than or equal to one. Kraft's inequality can be thought of in terms of a constrained budget to be ...
where L is the column length and N the number of theoretical plates. [5] The relation between plate number and peak width at the base is given by N = 16 ⋅ ( t R W b ) 2 {\displaystyle N=16\cdot \left({\frac {t_{R}}{W_{b}}}\right)^{2}\,} .