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Generator (mathematics) The 5th roots of unity in the complex plane under multiplication form a group of order 5. Each non-identity element by itself is a generator for the whole group. In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that ...
The BCH code with and higher has the generator polynomial. This code has minimal Hamming distance 15 and corrects 7 errors. It has 1 data bit and 14 checksum bits. It is also denoted as: (15, 1) BCH code. In fact, this code has only two codewords: 000000000000000 and 111111111111111 (a trivial repetition code ).
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 ...
An irreducible code is a cyclic code in which the code, as an ideal is irreducible, i.e. is minimal in , so that its check polynomial is an irreducible polynomial. Examples [ edit ] For example, if A = F 2 {\displaystyle A=\mathbb {F} _{2}} and n = 3 {\displaystyle n=3} , the set of codewords contained in cyclic code generated by ( 1 , 1 , 0 ...
Systematic code. In coding theory, a systematic code is any error-correcting code in which the input data are embedded in the encoded output. Conversely, in a non-systematic code the output does not contain the input symbols. Systematic codes have the advantage that the parity data can simply be appended to the source block, and receivers do ...
22 – Equalizer Circuit Breaker. 23 – Temperature control device, Heater. 24 – Volts per Hertz Relay. 25 – Synchronizing or Synchronism-check Device. 26 – Apparatus Thermal Device, Temperature Switch. 27 – Undervoltage Relay. 27P - Phase Undervoltage. 27S - DC Undervoltage Relay. 27TN - Third Harmonic Neutral Undervoltage.