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 Jun 12 comment How to find the 4th degree polynomial with given values at $0,1,2,3,4$? I think you mean q(1)=1. Oct 17 comment polynomial over finite field, roots forming additive subgroup The motivation by the way is proving a property of certain point sets in projective geometry over finite fields. A proof of this (even just the {0,w1,...,wt} part) can be completed by me to a good research article (web of science level). I will gladly offer coauthorship to whoever provides me with a proof. Oct 17 awarded Curious Oct 16 revised polynomial over finite field, roots forming additive subgroup added 7 characters in body Oct 16 comment polynomial over finite field, roots forming additive subgroup The $\{w_i | 1\le i\le t-1\}$ are a fixed set for which a polynomial $f$ with said properties exist. If it helps, it can be derived from the above properties that when writing $f(z)=\sum_{i=0}^{q-1} a_i z^i$ then $a_1=\sum_{i=1}^{t-1} w_i^{-1}$ and that $a_{2s+1}=0$ for all $s\ge 1$, and also that $a_{q-2}=0$. Oct 16 comment polynomial over finite field, roots forming additive subgroup I updated the problem statement even more. These $q/t+1$ sets all appear to be cosets of additive subgroups of size $t$ of $\mathbb{F}_q$. Oct 16 revised polynomial over finite field, roots forming additive subgroup added 69 characters in body Oct 16 awarded Commentator Oct 16 comment polynomial over finite field, roots forming additive subgroup You are right, I have probably cut out too much of the original problem. I have updated it to the full problem statement now. Oct 16 revised polynomial over finite field, roots forming additive subgroup added 417 characters in body Oct 16 asked polynomial over finite field, roots forming additive subgroup Oct 16 answered Is a Spread Unique? Oct 16 comment Number of vector and affine subspaces of dimension $k$ of $E$ over $\mathbb{F_q}$ I don't see what you want to prove... is $\mathcal E$ not equal to $(\mathbb{F}_q)^n$? Oct 16 answered Existence of a special set of q+2 points in the finite affine plane over $\mathbb F_q$ Sep 30 comment {0,1}-solutions for integer equations via lattice base reduction? Thanks! That second link seems to give an error though: Forbidden You don't have permission to access /~mec/Summer2009/meerkamp/Site/Solving_any_Sudoku_II.html on this server. Sep 21 answered Battle Ship Winning Algorithm - Optimal Strategy Sep 21 asked {0,1}-solutions for integer equations via lattice base reduction? Jun 24 comment Complement of all-one vector in binary vector space No, you are right, this doesn't work for every code. It luckily worked for this one, since it turns out that the only way to form the all-one vector from these minimum-weight code words is by summing up an odd number of them. Not exactly generally applicable thus. But more such possibilities are welcomed! Jun 24 answered Complement of all-one vector in binary vector space Jun 24 revised Complement of all-one vector in binary vector space added 363 characters in body