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Hamming (7,4) In coding theory, Hamming (7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950.
In mathematical terms, Hamming codes are a class of binary linear code. For each integer r ≥ 2 there is a code-word with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal ...
SIM lock. A SIM lock, simlock, network lock, carrier lock or ( master) subsidy lock is a technical restriction built into GSM and CDMA [ 1] mobile phones by mobile phone manufacturers for use by service providers to restrict the use of these phones to specific countries and/or networks. This is in contrast to a phone (retrospectively called SIM ...
Bootloader unlocking. Bootloader unlocking is the process of disabling the bootloader security that makes secure boot possible. It can make advanced customizations possible, such as installing a custom firmware. On smartphones this can be a custom Android distribution or another mobile operating system.
A personal unblocking key ( PUK ), sometimes called personal unblocking code ( PUC ), is used in SIM cards to reset a personal identification number (PIN) that has been lost or forgotten. Most mobile phones offer the feature of PIN protection. After switching on the phone, if the PIN security function is active, the user is required to enter a ...
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 ...
The Hamming(7,4) code may be written as a cyclic code over GF(2) with generator + +. In fact, any binary Hamming code of the form Ham(r, 2) is equivalent to a cyclic code, [3] and any Hamming code of the form Ham(r,q) with r and q-1 relatively prime is also equivalent to a cyclic code. [4]
Hamming weight. The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a string of bits, this is the number of 1's in the string, or the digit sum of the binary ...
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