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A problem in Galois Geometry

Given a prime $p$, out of $N$ vectors of length $p^k$ over $\Bbb F_2$ of Hamming weight $w^{k}$ that are chosen, how many vectors can there be with pairwise Hamming distance at least $2w^{k}$ given ...
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Effectiveness of the distinguished theta characteristic in characteristic 2

Let $k$ be an algebraically closed field of characteristic 2. Let $C$ be a (smooth projective connected) curve over $k$. Can there exist a rational function on $C$ whose differential is holomorphic ...
7
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3answers
247 views

Sets from $(F_2)^n$ which are not fixed by any non-identity isomorphism

This is a followup question to the discussion in the comments of Sets which are not fixed by any non-identity isomorphism So consider a finite $n$-dimensional vector space $V$ over $F_2$. For which ...
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285 views

Are these two subspaces of $\mathbb{Z}/2[[x]]$ the same?

The following questions arise from modular form theory. But this theory isn't needed to formulate or understand them, and I'm not using the modular-forms tag. NOTATION Fix an odd prime $N$. Let $$ ...