论文标题
减少规范跟踪代码
Decreasing norm-trace codes
论文作者
论文摘要
降低的规范跟踪代码是评估代码，由一组在分裂性下封闭的单元和扩展标准曲线的合理点。特别是，降低的规范跟踪代码包含扩展规范曲线上的单点代数几何（AG）代码。我们使用gröbner基础理论，并在曲线的有理点上找到指标函数，以确定降低规范跟踪代码的基本参数：长度，维度和最小距离。我们还获得了他们的双重代码。我们为降低规范跟踪代码的条件是自我实施或自动划分的代码。我们提供了一个线性精确的维修方案，以纠正单个擦除，以减少规范跟踪代码，该代码适用于速率代码，该方案比Jin，Luo和Xing（IEEE交易（IEEE交易）（IEEE TRASSACTION for INFORLION {\ bf 64}（2），900-908，2018）应用于单点AG时，AG AG代码超过了扩展范围。
The decreasing norm-trace codes are evaluation codes defined by a set of monomials closed under divisibility and the rational points of the extended norm-trace curve. In particular, the decreasing norm-trace codes contain the one-point algebraic geometry (AG) codes over the extended norm-trace curve. We use Gröbner basis theory and find the indicator functions on the rational points of the curve to determine the basic parameters of the decreasing norm-trace codes: length, dimension, and minimum distance. We also obtain their dual codes. We give conditions for a decreasing norm-trace code to be a self-orthogonal or a self-dual code. We provide a linear exact repair scheme to correct single erasures for decreasing norm-trace codes, which applies to higher rate codes than the scheme developed by Jin, Luo, and Xing (IEEE Transactions on Information Theory {\bf 64} (2), 900-908, 2018) when applied to the one-point AG codes over the extended norm-trace curve.
