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首页> 外文期刊>Designs, Codes and Crytography >Multidimensional quasi-twisted codes: equivalent characterizations and their relation to multidimensional convolutional codes
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Multidimensional quasi-twisted codes: equivalent characterizations and their relation to multidimensional convolutional codes

机译：多维准扭曲代码：等效特征及其与多维卷积码的关系

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摘要

We study multidimensional analogues of quasi-twisted codes from different points of view. Their concatenated structure allows us to characterize self-dual and complementary-dual classes of such codes as well as to show that multidimensional quasi-twisted (QT) codes are asymptotically good, together with their self-dual and complementary-dual subclasses. They are naturally related to nD convolutional codes as well. It is known that the minimum distance of quasi-cyclic codes provides a lower bound on the free distance of convolutional codes. An analogous result was shown for certain 1-generator 2D convolutional codes by using quasi-2D-cyclic codes. We prove a similar relation between convolutional codes and the related QT codes first, and then generalize the relation further to certain product convolutional codes and the related product QT codes, which improves the previous result in terms of dimension and number of generators. We also provide two-dimensional ternary and binary codes of modest lengths which yield good parameters.
机译：我们从不同的角度研究了准扭曲代码的多维类似物。它们的连接结构使我们能够表征自我双重和互补 - 双类别的这些代码，并表明多维准扭曲（QT）代码与其自我双重和互补 - 双子基组相同。它们与ND卷积规范自然有关。众所周知，准循环码的最小距离在卷积码的自由距离上提供下限。通过使用准2D循环码显示某些1发生器2D卷积码的类似结果。我们首先在卷积码和相关QT码之间证明类似的关系，然后概括了某些产品卷积码和相关产品QT代码的关系，这改善了先前的结果，以方面的维度和发电机的数量。我们还提供了适度长度的二维三元和二进制代码，其产生良好的参数。

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