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Decoding of binary Goppa codes is traditionally done by Patterson algorithm, which gives good error-correcting capability (it corrects all design errors), and is also fairly simple to implement. Patterson algorithm converts a syndrome to a vector of errors.
The rate of a code is inversely related to the query complexity, but the exact shape of this tradeoff is a major open problem. [8] [9] It is known that there are no LDCs that query the codeword in only one position, and that the optimal codeword size for query complexity 2 is exponential in the size of the original message. [8]
In software engineering, rubber duck debugging (or rubberducking) is a method of debugging code by articulating a problem in spoken or written natural language. The name is a reference to a story in the book The Pragmatic Programmer in which a programmer would carry around a rubber duck and debug their code by forcing themselves to explain it ...
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
if , decode code word to be all 0's if d H ≥ t + 1 {\displaystyle d_{H}\geq t+1} , decode code word to be all 1's This algorithm is a boolean function in its own right, the majority function .
A binary-to-text encoding is encoding of data in plain text. More precisely, it is an encoding of binary data in a sequence of printable characters . These encodings are necessary for transmission of data when the communication channel does not allow binary data (such as email or NNTP ) or is not 8-bit clean .
Since 7 October 2024, Python 3.13 is the latest stable release, and it and, for few more months, 3.12 are the only releases with active support including for bug fixes (as opposed to just for security) and Python 3.9, [55] is the oldest supported version of Python (albeit in the 'security support' phase), due to Python 3.8 reaching end-of-life.
As with ideal observer decoding, a convention must be agreed to for non-unique decoding. The maximum likelihood decoding problem can also be modeled as an integer programming problem. [1] The maximum likelihood decoding algorithm is an instance of the "marginalize a product function" problem which is solved by applying the generalized ...