In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless, we show that our construction yields several families of MDS codes. Further, for a large subclass of (MDS) twisted RS codes, we show that the new codes are not generalized RS codes. To achieve this, we use properties of Schur squares of codes as well as an explicit description of the dual of a large subclass of our codes. We conclude the paper with a description of a decoder, that performs very well in practice as shown by extensive simulation results.
翻译：在本条中,我们在Hamming指标中提出了新的评估代码结构,我们称之为扭曲的Reed-Solomon代码。虽然Reed-Solomon(RS)代码是MSDS代码,但扭曲的RSS代码则不必如此。然而,我们表明,我们的建筑生成了多种MDS代码的家庭。此外,对于一大小类(MDS)扭曲的RSS代码,我们表明,新的代码不是通用的RS代码。为了实现这一点,我们使用了Schur广场代码的特性,以及我们法典中大小类的双重特征。我们用解码器的描述来结束文件,而从广泛的模拟结果中可以看出,这在实际中表现非常好。
相关内容
- Today (iOS and OS X): widgets for the Today view of Notification Center
- Share (iOS and OS X): post content to web services or share content with others
- Actions (iOS and OS X): app extensions to view or manipulate inside another app
- Photo Editing (iOS): edit a photo or video in Apple's Photos app with extensions from a third-party apps
- Finder Sync (OS X): remote file storage in the Finder with support for Finder content annotation
- Storage Provider (iOS): an interface between files inside an app and other apps on a user's device
- Custom Keyboard (iOS): system-wide alternative keyboards
Source: iOS 8 Extensions: Apple’s Plan for a Powerful App Ecosystem
微信扫码咨询专知VIP会员