论文标题
多层纵横交错误和擦除校正
Multilayer crisscross error and erasure correction
论文作者
论文摘要
在这项工作中，考虑了多层纵横交错的误差和擦除，这会影响矩阵列表矩阵中的整个行和列。为了衡量此类错误和擦除，引入了多覆盖指标。得出了几个边界，包括单胎结合，最大的多覆盖距离（MMCD）代码定义为实现它的代码。研究了双重性，刺穿和缩短线性MMCD代码。结果表明，线性MMCD代码的双重不一定是MMCD，并且满足这种偶性条件的二重性被定义为双重MMCD代码。最后，给出了多封元度量中代码的某些构造，包括双重MMCD代码，以及有效的解码算法。
In this work, multilayer crisscross error and erasures are considered, which affect entire rows and columns in the matrices of a list of matrices. To measure such errors and erasures, the multi-cover metric is introduced. Several bounds are derived, including a Singleton bound, and maximum multi-cover distance (MMCD) codes are defined as those attaining it. Duality, puncturing and shortening of linear MMCD codes are studied. It is shown that the dual of a linear MMCD code is not necessarily MMCD, and those satisfying this duality condition are defined as dually MMCD codes. Finally, some constructions of codes in the multi-cover metric are given, including dually MMCD codes, together with efficient decoding algorithms for them.
