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A code is defined to be equidistant if and only if there exists some constant d such that the distance between any two of the code's distinct codewords is equal to d. [4] In 1984 Arrigo Bonisoli determined the structure of linear one-weight codes over finite fields and proved that every equidistant linear code is a sequence of dual Hamming codes .
Computers typically use binary arithmetic, but to make the example easier to read, it will be given in decimal. Suppose we are using six-digit decimal floating-point arithmetic, sum has attained the value 10000.0, and the next two values of input[i] are 3.14159 and 2.71828. The exact result is 10005.85987, which rounds to 10005.9.
A block code (specifically a Hamming code) where redundant bits are added as a block to the end of the initial message A continuous convolutional code where redundant bits are added continuously into the structure of the code word. The two main categories of ECC codes are block codes and convolutional codes.
The description above is given for what is now called a serially concatenated code. Turbo codes, as described first in 1993, implemented a parallel concatenation of two convolutional codes, with an interleaver between the two codes and an iterative decoder that passes information forth and back between the codes. [6]
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
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The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix.This is a matrix such that () = holds for all {,}, where the message is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field.