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A generator matrix for a Reed–Muller code RM (r, m) of length N = 2m can be constructed as follows. Let us write the set of all m -dimensional binary vectors as:
A generator matrix for a linear -code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).
A new study found that a healthy diet may produce lower blood glucose levels and reduce the risk of type 2 diabetes in men regardless of any genetic predisposition to the condition.
The annual inflation rate for goods is now 0.1%. What matters most to consumers isn’t the inflation number attached to any particular product; it’s how much their paycheck buys. Here, the news ...
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The second of two U.S. citizens to be reported as missing in the Greek Isles has been found dead, according to ABC News.
The Gilbert–Varshamov bound for linear codes is related to the general Gilbert–Varshamov bound, which gives a lower bound on the maximal number of elements in an error-correcting code of a given block length and minimum Hamming weight over a field . This may be translated into a statement about the maximum rate of a code with given length ...
Reports of American consumers’ inability to pay their bills—or their waning interest in shopping—are greatly exaggerated.