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Questions about the properties of vector spaces and linear transformations, including linear systems in general.
2
votes
Compressing a system of linear equations
I think I got what you mean. Please correct me if I misunderstand your question.
So, I think "$0 < \vert M_i\vert < m$" in the description of property $\Gamma$ should read "$0 < \vert M_i\vert \leq k …
2
votes
Accepted
Function (/matrix) to generate linearly independent vectors.
I don't quite follow the first paragraph of your question. But reading the rest of your post, if you only need a set $S$ of $N$ $m$-dimensional vectors over the finite field of some small order in whi …
7
votes
Almost Hadamard matrices
If you regard each row of your desired matrix as a sequence of bipolar signals and each column as a time frame, then, with one additional condition that the matrix is circulant, what you're asking bec …
1
vote
Doing column permutation under row overlap constraint
I doubt there is a particular algorithm worth mentioning for avoiding $2 \times 2$ all-one submatrices (or better known as $4$-cycles in the context of LDPC codes) in parity-check matrices which is sp …
3
votes
Accepted
Ranks of higher incidence matrices of designs
For the generalization in the first direction, the $p$-rank of the incidence matrix $N$ of an $S(2,k,v)$ is lower bounded by the dimension of the Steinberg module:
$$\operatorname{rank}_2(N)(\operato …
4
votes
Accepted
On MDS code property
I guess you exclude trivial MDS codes, generalized Reed-Solomon codes, and MDS codes that can be obtained by code extension.
If you exclude them all, there are still a bunch of MDS codes. In general, …