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Proof. We need to prove that if you add a burst of length to a codeword (i.e. to a polynomial that is divisible by ()), then the result is not going to be a codeword (i.e. the corresponding polynomial is not divisible by ()).
Verhoeff's notes that the particular permutation, given above, is special as it has the property of detecting 95.3% of the phonetic errors. [8] The strengths of the algorithm are that it detects all transliteration and transposition errors, and additionally most twin, twin jump, jump transposition and phonetic errors.
Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
A type II error, or a false negative, is the erroneous failure in bringing about appropriate rejection of a false null hypothesis. [1] Type I errors can be thought of as errors of commission, in which the status quo is erroneously rejected in favour of new, misleading information. Type II errors can be thought of as errors of omission, in which ...
Pydoc is the standard documentation module for the programming language Python. Similar to the functionality of Perldoc within Perl and Javadoc within Java, Pydoc allows Python programmers to access Python's documentation help files, generate text and HTML pages with documentation specifics, and find the appropriate module for a particular job. [1]
That these codes allow indeed for quantum computations of arbitrary length is the content of the quantum threshold theorem, found by Michael Ben-Or and Dorit Aharonov, which asserts that you can correct for all errors if you concatenate quantum codes such as the CSS codes—i.e. re-encode each logical qubit by the same code again, and so on, on ...
The null coalescing operator is a binary operator that is part of the syntax for a basic conditional expression in several programming languages, such as (in alphabetical order): C# [1] since version 2.0, [2] Dart [3] since version 1.12.0, [4] PHP since version 7.0.0, [5] Perl since version 5.10 as logical defined-or, [6] PowerShell since 7.0.0, [7] and Swift [8] as nil-coalescing operator.
Thomas Nicely, a professor of mathematics at Lynchburg College, had written code to enumerate primes, twin primes, prime triplets, and prime quadruplets.Nicely noticed some inconsistencies in the calculations on June 13, 1994, shortly after adding a Pentium system to his group of computers, but was unable to eliminate other factors (such as programming errors, motherboard chipsets, etc.) until ...