3
votes
0answers
138 views

What is the function like when its Mobius inversion is $\sum_{w|r, (w,t)=1}\mu(w)q^{r/w}$?

Everyone, I am now reading a paper named The Irreducible Factors of $(cx+d)x^{q^m}-(ax+b)$ over $GF(q)$, http://qjmath.oxfordjournals.org/content/14/1/61.extract. And I’m confused with one of its ...
2
votes
1answer
270 views

Finding a subspace disjoint from a union of subspaces

Let $k$ be a finite field (I care about $\mathbb F_p$, especially $\mathbb F_2$) and let $V_1,...,V_N\subset k^n$ be subspaces. I want to find a subspace $S\subset k^n$ such that $S\cap V_i=0$ for ...
4
votes
0answers
286 views

Matching a binary matrix

Given a MxN 0-1 matrix D, with the property that both M and N are odd numbers its row sums and column sums in the $\mathbb{Z}_2$ field are all equal to the same number (0 or 1). How do we find M ...
1
vote
1answer
417 views

Number of subset sums

Let $\mathbb{F}_q$ be a finite field with characteristic $p$ and $p < q$ (i.e. not a prime field). Let $D\subseteq \mathbb{F}_q$ be a some set with $|D|=n$. Find a non-empty subset ...