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Results tagged with finite-fields
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user 27829
A finite field is a field with a finite number of elements. For each prime power $q^k$, there is a unique (up to isomorphism) finite field with $q^k$ elements. Up to isomorphism, these are the only finite fields.
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, …
- 3,692
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 …
- 3,692
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 …
- 3,692