论文标题
许多来自任意代数曲线属的非固定溶剂型MDS代码
Many Non-Reed-Solomon Type MDS Codes From Arbitrary Genus Algebraic Curves
论文作者
论文摘要
在编码理论和有限的几何形状中构造非固体固体型MDS代码总是很有趣且重要。在本文中，我们证明了来自任意代数曲线的非修复固体型MDS代码。事实证明，来自较高属曲线的MDS代数几何（Ag）代码不等于较低属曲线的MDS AG代码。对于一个属，我们构建了来自椭圆曲线的连续长度的MDS AG代码。还构建了椭圆曲线的新的自dual MDS AG代码$ {\ bf f} _ {2^s} $。这些MDS AG代码不等于Reed-Solomon代码，不等于已知的MDS扭曲的Reed-Solomon代码，也不等于Roth-lempel MDS代码。 因此，许多非等效的MDS AG代码不等于芦苇 - 固体代码和已知的MDS扭曲折叠 - 固体代码，可以从任意代数属曲线中获得。从最大曲线中构建明显的更长的MDS AG代码是有趣的开放问题。
It is always interesting and important to construct non-Reed-Solomon type MDS codes in coding theory and finite geometries. In this paper, we prove that there are non-Reed-Solomon type MDS codes from arbitrary genus algebraic curves. It is proved that MDS algebraic geometry (AG) codes from higher genus curves are not equivalent to MDS AG codes from lower genus curves. For genus one case, we construct MDS AG codes of small consecutive lengths from elliptic curves. New self-dual MDS AG codes over ${\bf F}_{2^s}$ from elliptic curves are also constructed. These MDS AG codes are not equivalent to Reed-Solomon codes, not equivalent to known MDS twisted Reed-Solomon codes and not equivalent to Roth-Lempel MDS codes. Hence many non-equivalent MDS AG codes, which are not equivalent to Reed-Solomon codes and known MDS twisted-Reed-Solomon codes, can be obtained from arbitrary genus algebraic curves. It is interesting open problem to construct explicit longer MDS AG codes from maximal curves.
