Find the smallest $n$ and $m$
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Suppose $F$ is a finite field with $q$ element and the numbers $k$ and $s$ are given. I want to build a matrix over $F$ with $n$ row and $m$ column such that every $k$ columns of this matrix are linearly independent. Now find the smallest $n$ and $m$ in term of $s$ and $k$ and $q$ such that satisfies in my condition and also we must have $m > s $ and $m = s+n$
linear-algebra
asked Jan 4 at 16:04
ebadebad
165
$endgroup$
add a comment |
$begingroup$
Suppose $F$ is a finite field with $q$ element and the numbers $k$ and $s$ are given. I want to build a matrix over $F$ with $n$ row and $m$ column such that every $k$ columns of this matrix are linearly independent. Now find the smallest $n$ and $m$ in term of $s$ and $k$ and $q$ such that satisfies in my condition and also we must have $m > s $ and $m = s+n$
linear-algebra
asked Jan 4 at 16:04
ebadebad
165
$endgroup$
$begingroup$
Does every $k$ columns are linearly independent mean that every set of $k$ columns is linearly independent, or that blocks of $k$ columns are independent?
$endgroup$
– tch
Jan 4 at 16:15
$begingroup$
It means every set of k columns are linearly independent
$endgroup$
– ebad
Jan 4 at 16:31
add a comment |
$begingroup$
Suppose $F$ is a finite field with $q$ element and the numbers $k$ and $s$ are given. I want to build a matrix over $F$ with $n$ row and $m$ column such that every $k$ columns of this matrix are linearly independent. Now find the smallest $n$ and $m$ in term of $s$ and $k$ and $q$ such that satisfies in my condition and also we must have $m > s $ and $m = s+n$
linear-algebra
asked Jan 4 at 16:04
ebadebad
165
$endgroup$
Suppose $F$ is a finite field with $q$ element and the numbers $k$ and $s$ are given. I want to build a matrix over $F$ with $n$ row and $m$ column such that every $k$ columns of this matrix are linearly independent. Now find the smallest $n$ and $m$ in term of $s$ and $k$ and $q$ such that satisfies in my condition and also we must have $m > s $ and $m = s+n$
linear-algebra
linear-algebra
asked Jan 4 at 16:04
ebadebad
165
asked Jan 4 at 16:04
ebadebad
165
asked Jan 4 at 16:04
ebadebad
165
asked Jan 4 at 16:04
ebadebad
165
asked Jan 4 at 16:04
ebadebad
165
165
$begingroup$
Does every $k$ columns are linearly independent mean that every set of $k$ columns is linearly independent, or that blocks of $k$ columns are independent?
$endgroup$
– tch
Jan 4 at 16:15
$begingroup$
It means every set of k columns are linearly independent
$endgroup$
– ebad
Jan 4 at 16:31
add a comment |
$begingroup$
Does every $k$ columns are linearly independent mean that every set of $k$ columns is linearly independent, or that blocks of $k$ columns are independent?
$endgroup$
– tch
Jan 4 at 16:15
$begingroup$
It means every set of k columns are linearly independent
$endgroup$
– ebad
Jan 4 at 16:31
$begingroup$
Does every $k$ columns are linearly independent mean that every set of $k$ columns is linearly independent, or that blocks of $k$ columns are independent?
$endgroup$
– tch
Jan 4 at 16:15
$begingroup$
Does every $k$ columns are linearly independent mean that every set of $k$ columns is linearly independent, or that blocks of $k$ columns are independent?
$endgroup$
– tch
Jan 4 at 16:15
$begingroup$
It means every set of k columns are linearly independent
$endgroup$
– ebad
Jan 4 at 16:31
$begingroup$
It means every set of k columns are linearly independent
$endgroup$
– ebad
Jan 4 at 16:31
add a comment |
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$begingroup$
Does every $k$ columns are linearly independent mean that every set of $k$ columns is linearly independent, or that blocks of $k$ columns are independent?
$endgroup$
– tch
Jan 4 at 16:15
$begingroup$
It means every set of k columns are linearly independent
$endgroup$
– ebad
Jan 4 at 16:31