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As pointed out by Snowball, the problem is inherently hard, see here and also here.. However, it can be done much faster in general than generating all the codewords.
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According to this page, there should be a code of length 20 with hamming distance 6 and between 2048-2279 codewords (or in other words, that contains at least $2^{11}$ words, meaning that data with 11 bits could be transmitted within blocks of 20 with HD 6).
3. Given a set C C of codewords, before we can construct a generator matrix, we need to verify that C C is a linear subspace - ie, the sum (and also scalar multiples in the non-binary case) of any two codewords must be a codeword. In the link given, the subsets C C given are all subspaces. The rows of the generator matrix G G can be taken to be ...
Finding generator matrix for binary linear code given parity check matrix. Ask Question Asked 9 years ago.
Generator matrix for linear [8, 5, 3] [8, 5, 3] -code. Consider the binary linear (13, 64, 5) (13, 64, 5) -code C3 C 3, or a [13, 6, 5] [13, 6, 5] -code. Then, let M M be the generator matrix for C3 C 3, such that we can rearrange the coordinate positions of the words in C3 C 3 so that M M is in the form: [1 1 1 G1 1 1 0 0 0 0 0 G2 0 0 0] [1 1 ...
For example a generator matrix of a binary Simplex code of dimension $4$ is given by $$\begin{pmatrix} 1 ...
My question is how do I find the standard generator matrix of a binary [7,6,2] code? From what I ...
1 Answer. Sorted by: 2. Yes, you can find the generator matrix through finding the kernel of H H, but you can find it through writing H H in its standard form, i.e., H =[A|In×k] H = [A | I n × k]. Then you use A A to build your generator matrix (in its standard form): G =[Ik|At] G = [I k | A t], where At A t is the transpose of the matrix A A ...
For a cyclic code with generator polynomial g(x) = g0 +g1x + … +grxr g (x) = g 0 + g 1 x + … + g r x r, the generator matrix is. where blank spaces represent 0 0. The generator matrix has dimensions k × n k × n, where k k is the dimension of the code and n n is the length of the code. A couple options for finding the parity check matrix: