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Features. [edit] Isabelle is generic: it provides a meta-logic(a weak type theory), which is used to encode object logics like first-order logic(FOL), higher-order logic(HOL) or Zermelo–Fraenkel set theory(ZFC). The most widely used object logic is Isabelle/HOL, although significant set theory developments were completed in Isabelle/ZF.
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.).
Traditional Reed–Muller codes are binary codes, which means that messages and codewords are binary strings. When r and m are integers with 0 ≤ r ≤ m, the Reed–Muller code with parameters r and m is denoted as RM ( r , m ). When asked to encode a message consisting of k bits, where holds, the RM ( r , m) code produces a codeword ...
RISC OS—Reduced Instruction Set Computer Operating System; RJE—Remote Job Entry; RLE—Run-Length Encoding; RLL—Run-Length Limited; rmdir—remove directory; RMI—Remote Method Invocation; RMS—Richard Matthew Stallman; ROM—Read-Only Memory; ROMB—Read-Out Motherboard; ROM-DOS—Read-Only Memory – Disk Operating System; RPA ...
Open-source software is a prominent example of open collaboration, meaning any capable user is able to participate online in development, making the number of possible contributors indefinite. The ability to examine the code facilitates public trust in the software. [ 3]
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The distance of the concatenated code Cout ∘ Cin is at least dD, that is, it is a [ nN, kK, D '] code with D ' ≥ dD . Proof: Consider two different messages m1 ≠ m2 ∈ BK. Let Δ denote the distance between two codewords. Then. Thus, there are at least D positions in which the sequence of N symbols of the codewords Cout ( m1) and Cout ...
The attacker knows ^, the generator matrix of an (,) code ^ that is combinatorially able to correct errors. The attacker may ignore the fact that C ^ {\displaystyle {\hat {C}}} is really the obfuscation of a structured code chosen from a specific family, and instead just use an algorithm for decoding with any linear code.