论文标题
关于最小的子空间ZP-NULL设计
On minimal subspace Zp-null designs
论文作者
论文摘要
让$ Q $是Prime $ P $的功率，让$ v $是$ n $二维的空间，而现场gf $（q）$。 A $Z_p$-valued function $C$ on the set of $k$-dimensional subspaces of $V$ is called a $k$-uniform $Z_p$-null design of strength $t$ if for every $t$-dimensional subspace $y$ of $V$ the sum of $C$ over the $k$-dimensional superspaces of $y$ equals $0$.对于$ q = p = 2 $和$ 0 \ le t <k <n $，我们证明了非void $ k $ - 均匀的最小二方数，$ k $ z_p $ z_p $ -null强度$ t $ t $等于$ 2^{t+1} $。对于$ q> 2 $，我们给出了该数字的下限和上限。
Let $q$ be a power of a prime $p$, and let $V$ be an $n$-dimensional space over the field GF$(q)$. A $Z_p$-valued function $C$ on the set of $k$-dimensional subspaces of $V$ is called a $k$-uniform $Z_p$-null design of strength $t$ if for every $t$-dimensional subspace $y$ of $V$ the sum of $C$ over the $k$-dimensional superspaces of $y$ equals $0$. For $q=p=2$ and $0\le t<k<n$, we prove that the minimum number of non-zeros of a non-void $k$-uniform $Z_p$-null design of strength $t$ equals $2^{t+1}$. For $q>2$, we give lower and upper bounds for that number.
