论文标题
卷积代码的广义重量
Generalized weights of convolutional codes
论文作者
论文摘要
1997年，罗森塔尔（Rosenthal）和约克（York）将卷积代码定义为卷积代码的广义锤量重量，将卷积代码作为无限尺寸线性代码，并赋予了锤式指标。在本文中，我们提出了卷积代码的广义权重的新定义，该定义考虑了代码的基础模块结构。我们得出了广义权重的基本特性，并讨论了与先前定义的关系。我们在MDS和MDP代码的重量层次结构上建立上限，并表明，根据代码参数，MDS代码的某些广义权重由代码的长度，等级和内部程度确定。我们还证明了卷积代码结合的抗模具，并将最佳码头定义为符合抗模子结合的代码。最后，我们对最佳码头进行分类并计算其重量层次结构。
In 1997 Rosenthal and York defined generalized Hamming weights for convolutional codes, by regarding a convolutional code as an infinite dimensional linear code endowed with the Hamming metric. In this paper, we propose a new definition of generalized weights of convolutional codes, that takes into account the underlying module structure of the code. We derive the basic properties of our generalized weights and discuss the relation with the previous definition. We establish upper bounds on the weight hierarchy of MDS and MDP codes and show that that, depending on the code parameters, some or all of the generalized weights of MDS codes are determined by the length, rank, and internal degree of the code. We also prove an anticode bound for convolutional codes and define optimal anticodes as the codes which meet the anticode bound. Finally, we classify optimal anticodes and compute their weight hierarchy.
