论文标题
新的极端二元二进制自偶长68的自我双重代码，从新颖的方法到邻居
New Extremal binary self-dual codes of length 68 from a novel approach to neighbors
论文作者
论文摘要
在这项工作中，我们介绍了自偶代码之间距离的概念，该代码概括了邻居的自我偶尔代码的概念。使用K-Neighbors，我们能够构建具有新的重量枚举器的长度68的极端二进制自偶代码。我们构造了143个长度68的极端二进制自偶代码，其中枚举了新的重量，其中包括42个代码，其w_ {68,2}中的gamma = 8和40在其W_ {68,2}中gamma = 9。这些示例是这些伽马值的文献中的第一个。这完成了w_ {68,2}中伽玛可能值的理论列表。
In this work, we introduce the concept of distance between self-dual codes, which generalizes the concept of a neighbor for self-dual codes. Using the k-neighbors, we are able to construct extremal binary self-dual codes of length 68 with new weight enumerators. We construct 143 extremal binary self-dual codes of length 68 with new weight enumerators including 42 codes with gamma=8 in their W_{68,2} and 40 with gamma=9 in their W_{68,2}. These examples are the first in the literature for these gamma values. This completes the theoretical list of possible values for gamma in W_{68,2}.
