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Results tagged with linear-algebra
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user 34180
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
3
votes
On MDS code property
It has been proved by Simeon Ball that for $k \leq p$, all $[n, k, n-k+1]_q$ codes are Reed-Solomon codes, where $q = p^h$. See Corollary 9.2 in the following paper:
Ball, S. On sets of vectors of a …
- 1,197
5
votes
0
answers
232
views
A question on hyperplanes in partial linear spaces and hypergraphs
A partial linear space (or a linear hypergraph) is a point line geometry $(P,L,I)$ where for every pair of points there is at most one line incident with both of them. A hyperplane in a partial linear …
- 1,197
4
votes
2
answers
380
views
Finding the set of all $0$-$1$ vectors in an affine subspace
We are given a $0$-$1$ matrix $A$ with constant row and column sum, and we need to find out if there exists a $0$-$1$ vector in the solution space of $Ax = \mathbf{1}$ over $\mathbb{Q}$ (or $\mathbb{Z …
- 1,197
4
votes
Linear algebra proofs in combinatorics?
Here are some examples where the dimension of a vector space of polynomials is used to solve a combinatorial problem.
Theorem 1 There are at most $n(n+1)/2$ equiangular lines in $\mathbb{R}^n$.
Proof. …