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In mathematics and computer science, the binary Goppa code is an error-correcting code that belongs to the class of general Goppa codes originally described by Valerii Denisovich Goppa, but the binary structure gives it several mathematical advantages over non-binary variants, also providing a better fit for common usage in computers and ...
To construct the binary-reflected Gray code iteratively, at step 0 start with the =, and at step > find the bit position of the least significant 1 in the binary representation of and flip the bit at that position in the previous code to get the next code . The bit positions start 0, 1, 0, 2, 0, 1, 0, 3, ....
Such a decoding algorithm requires not just knowing , in the sense of knowing an arbitrary generator matrix, but requires one to know the parameters used when specifying in the chosen family of codes. For instance, for binary Goppa codes, this information would be the Goppa polynomial and the code locators.
The Source coding theorem states that for any ε > 0, i.e. for any rate H(X) + ε larger than the entropy of the source, there is large enough n and an encoder that takes n i.i.d. repetition of the source, X 1:n, and maps it to n(H(X) + ε) binary bits such that the source symbols X 1:n are recoverable from the binary bits with probability of ...
Zemor's algorithm is based on a type of expander graphs called Tanner graph.The construction of code was first proposed by Tanner. [3] The codes are based on double cover, regular expander , which is a bipartite graph.
Concise Binary Object Representation (CBOR) is a binary data serialization format loosely based on JSON authored by Carsten Bormann and Paul Hoffman. [a] Like JSON it allows the transmission of data objects that contain name–value pairs, but in a more concise manner. This increases processing and transfer speeds at the cost of human readability.
Video signals are usually encoded into binary digit (0, 1) or seven digit pulse-code modulation (PCM), which is a method used to digitally represent original video signal. . The video signal converted to binary digit PCM at the point of origin can be then transmitted over existing telephone cable or wire directly to the destination
Understanding this more nuanced reality is crucial for executives navigating the AI landscape—we need to move beyond the binary question of whether AI has reached human-level intelligence and ...