论文标题
完美的代码纠正一爆的有限级错误错误
Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors
论文作者
论文摘要
通过应用于DNA存储，闪存和磁性记录的动机，我们研究了有限型误差通道的完美爆发校正代码。这些代码是用适当的错误球铺平整数网格的晶格。我们构建了两类这样的完美代码，以校正单次长度$ 2 $的$（1,0）$ - 有限级错误错误，包括循环和非循环爆发。我们还提出了一种通用结构，该结构需要具有特定属性的有限字段中的原始元素。然后，我们证明存在各种参数式，因此存在这些原始元素，因此，存在许多完美的爆发校正代码。
Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error ball. We construct two classes of such perfect codes correcting a single burst of length $2$ for $(1,0)$-limited-magnitude errors, both for cyclic and non-cyclic bursts. We also present a generic construction that requires a primitive element in a finite field with specific properties. We then show that in various parameter regimes such primitive elements exist, and hence, infinitely many perfect burst-correcting codes exist.
