AI 中文总结
研究德萨格展布码最近邻解码器在超过半最小距离时的解码能力，开发新算法可在有插入和删除情况下唯一解码，当删除维数至多为\(k - 2\)时能成功解码，还提出两种改进方法。
AI 中文摘要
展布码是一类著名的常维子空间度量码。对于常维数\(k\)且环境空间维数\(n\)是\(k\)的倍数的情况，这些码具有最小距离\(2k\)和丰富的几何结构。本文研究了德萨格展布码最近邻解码器的解码能力，证明了在超过半最小距离时仍可实现唯一解码。基于此，开发了一种新的解码算法，可在存在插入和删除的情况下唯一解码德萨格展布码，插入和删除分别会增加和减少传输码字的维数。即使插入和删除的维数之和超过半最小距离，只要删除的维数至多为\(k - 2\)，该算法就能以较小的解码失败率成功解码。还提出了该算法的两种改进方法，经实验，它们能处理几乎与最近邻解码器一样多的插入。
英文摘要
Spread codes are a well-known family of constant-dimension subspace-metric codes. For constant dimension $k$ and ambient space dimension $n$ being a multiple of $k$, these codes have minimum distance $2k$ and a rich geometric structure. In this paper, we study the decoding capabilities of the Nearest Neighbor Decoder for Desarguesian spread codes, establishing that unique decoding is still achievable beyond half the minimum distance. Motivated by this, we develop a new decoding algorithm to uniquely decode Desarguesian spread codes in the presence of both insertions and deletions, which increase and decrease, respectively, the dimension of the transmitted codeword. Even when the sum of the dimensions of insertions and deletions exceeds half the minimum distance, provided that deletions are of dimension at most $k-2$, the algorithm succeeds with a small decoding failure. We also propose two refinements to this algorithm that, empirically, can handle nearly as many insertions as the Nearest Neighbor Decoder.
