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The definition of a generator appears identical to that of a function, except the keyword yield is used in place of return. However, a generator is an object with persistent state, which can repeatedly enter and leave the same scope. A generator call can then be used in place of a list, or other structure whose elements will be iterated over.
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 ()).
The basic idea of majority logic decoding is to build several checksums for each received code word element. Since each of the different checksums must all have the same value (i.e. the value of the message word element weight), we can use a majority logic decoding to decipher the value of the message word element.
If she sent her phone number in pieces, asking Bob to acknowledge receipt of each piece, at least four messages would have to be sent anyway (two from Alice, and two acknowledgments from Bob). So the erasure code in this example, which requires five messages, is quite economical. This example is a little bit contrived.
In all, W comprises 4096 = 2 12 elements. The elements of W are called code words. They can also be described as subsets of a set of 24 elements, where addition is defined as taking the symmetric difference of the subsets. In the extended binary Golay code, all code words have Hamming weights of 0, 8, 12, 16, or 24.
Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of Python 2. [37] Python consistently ranks as one of the most popular programming languages, and has gained widespread use in the machine learning community. [38] [39] [40] [41]
The complete weight enumerator of the extended ternary Golay code is + + + (+ +) + (+ +). The automorphism group of the extended ternary Golay code is 2. M 12, where M 12 is the Mathieu group M 12.
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.