2016年3月5日 · Given a linear code C with generator matrix G and parity matrix H. Would permuting rows and/or columns of these matricies produce a different linear code? I am under the impression that the resulting linear code would be equivalent to the original linear code.

2018年6月13日 · We can still work with the definition of parity check matrix, though. We want something that sends any combination of these rows to zero, so we can solve $\begin{bmatrix} G & | & \bf{0} \end{bmatrix}$ where $\bf{0}$ is a column vector of all zeroes.

2019年12月2日 · I have an extremely basic question about Parity Check Matrix. Let's call it H and consider a codeword: I have been told that through H we may verify if it is a real codeword or not (and consider the case it is). Precisely, if the product c*H' = 0 (where ' denotes transpose), it is a true codeword (I read this sentence here, on slide 5).

2018年8月17日 · (1) Find the generator matrix $\mathbf G $,and parity check matrix $\mathbf H$. (2) Decode the following received vectors on a binary symmetric channel (with a crossover probability $𝑝 < 1/2$) by using syndrome decoding: $$𝑦_1 = (01101011),\,𝑦_2 = (00010110).$$ (3) Decode again using the maximum-likelihood decoding.

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2016年11月20日 · Parity Matrix. Adding respectively an extra row or column to a table so that the parity of all columns or rows respectively is odd or even is always straightforward. Adding both at once adds one extra cell that is overspecified (at the intersection of extra column and row - at bottom right hand corner if we extend in length and to the right).

2013年4月12日 · Note that I prefer to construct the parity check matrix first, and then deduce a matrix for the code, using exactly the same trick as rschwieb. (My parity check matrix is the transpose of his.) Constructing the parity check matrix first has some advantages IMHO, such as yielding directly immediately that the code is cyclic.

pay attention to bit 0, totally only 1 bit for each row and one in all other rows. so don't be confused if sometimes you might find p4 or parity 4. it would be p4 = \begin{matrix}1\\1\\1\\0\\\end{matrix}

It can never correct double errors according to the Singleton Bound. I don't know what code is your Parity Check Matrix from; it certainly has a Singleton Bound of 5. Now you need to get the Generator Matrix to write the Syndrome table. $\endgroup$ –

2016年12月13日 · Finding the parity-check matrix of a generator matrix in $\Bbb F_3$. 2 How to get the parity check matrix if I don't have an identity matrix in my generator matrix?