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The RM(0, m) code is the repetition code of length N =2 m and weight N = 2 m−0 = 2 m−r. By 1 (,) = and has weight 1 = 2 0 = 2 m−r. The article bar product (coding theory) gives a proof that the weight of the bar product of two codes C 1, C 2 is given by
Type II codes are binary self-dual codes which are doubly even. Type III codes are ternary self-dual codes. Every codeword in a Type III code has Hamming weight divisible by 3. Type IV codes are self-dual codes over F 4. These are again even. Codes of types I, II, III, or IV exist only if the length n is a multiple of 2, 8, 4, or 2 respectively.
These "rate-distortion" models [107] suggest that the genetic code originated as a result of the interplay of the three conflicting evolutionary forces: the needs for diverse amino acids, [108] for error-tolerance [103] and for minimal resource cost. The code emerges at a transition when the mapping of codons to amino acids becomes nonrandom.
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix .This is a matrix such that () = holds for all {,}, where the message is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field.
U.S. NRC image of a modern steam turbine generator (STG). In electricity generation, a generator [1] is a device that converts motion-based power (potential and kinetic energy) or fuel-based power (chemical energy) into electric power for use in an external circuit.
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