论文标题
在cosets上的重量分布中，偶然扩展的芦苇 - 固体代码编码4
On cosets weight distributions of the doubly-extended Reed-Solomon codes of codimension 4
论文作者
论文摘要
我们将$ [Q+1，Q-3,5] _Q3 $ concoimension $ 4 $的概括性扩展的芦苇 - 固体代码作为与扭曲的立方相关的代码，在投射空间$ \ mathrm {pg}（3，q）$中。基于$ \ mathrm {pg}（3，q）$的点平面入射率矩阵，我们在所有考虑的代码的所有cosets中获得了3个权重3向量的数量。这使我们能够通过其重量分布分类并获取这些分布来对摇合物进行分类。 coset的重量是coset中任何向量的最小锤击重量。对于具有不同权重分布的同等重量的Zets，我们证明分布的$ W $ th组件（$ 3 <w \ le Q+1 $）之间的差异取决于$ 3 $ -RD组件之间的差异。这意味着对所获得的分布的有趣（在某种意义上是意外的）对称性。
We consider the $[q+1,q-3,5]_q3$ generalized doubly-extended Reed-Solomon code of codimension $4$ as the code associated with the twisted cubic in the projective space $\mathrm{PG}(3,q)$. Basing on the point-plane incidence matrix of $\mathrm{PG}(3,q)$, we obtain the number of weight 3 vectors in all the cosets of the considered code. This allows us to classify the cosets by their weight distributions and to obtain these distributions. The weight of a coset is the smallest Hamming weight of any vector in the coset. For the cosets of equal weight having distinct weight distributions, we prove that the difference between the $w$-th components, $3<w\le q+1$, of the distributions is uniquely determined by the difference between the $3$-rd components. This implies an interesting (and in some sense unexpected) symmetry of the obtained distributions.
