论文标题
在带有线性预测的添加剂MDS代码上
On additive MDS codes with linear projections
论文作者
论文摘要
我们支持一些证据表明，有限字段上长的添加剂MDS代码必须等同于线性代码。更准确地说，让$ c $为$ \ mathbb f_q $ -linear $（n，q^{hk}，n-k+1）_ {q^h} $ mds代码$ \ mathbb f_ {q^h} $。 If $k=3$, $h \in \{2,3\}$, $n > \max \{q^{h-1},h q -1\} + 3$, and $C$ has three coordinates from which its projections are equivalent to linear codes, we prove that $C$ itself is equivalent to a linear code.如果$ k> 3 $，$ n> q+k $，并且有两个坐标的两种不相交的子集，它们的组合大小最多为$ k-2 $，$ c $的预测相当于线性代码，我们证明$ c $等于代码，该代码与$ \ nathbb f_q $更大的字段相比是线性的。
We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let $C$ be an $\mathbb F_q$-linear $(n,q^{hk},n-k+1)_{q^h}$ MDS code over $\mathbb F_{q^h}$. If $k=3$, $h \in \{2,3\}$, $n > \max \{q^{h-1},h q -1\} + 3$, and $C$ has three coordinates from which its projections are equivalent to linear codes, we prove that $C$ itself is equivalent to a linear code. If $k>3$, $n > q+k$, and there are two disjoint subsets of coordinates whose combined size is at most $k-2$ from which the projections of $C$ are equivalent to linear codes, we prove that $C$ is equivalent to a code which is linear over a larger field than $\mathbb F_q$.
