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    Information coding by algebraic geometric code offering two decoding options
    58.
    发明授权
    Information coding by algebraic geometric code offering two decoding options 失效
    通过代数几何代码提供信息编码，提供两种解码选项

    公开(公告)号：US07634711B2

    公开(公告)日：2009-12-15

    申请号：US10825283

    申请日：2004-04-16

    Applicant: Philippe Piret ,  Frédéric Lehobey

    Inventor： Philippe Piret ,  Frédéric Lehobey

    IPC: H03M13/00

    CPC classification number: H04L1/0041 ,  H03M13/132 ,  H03M13/15 ,  H03M13/151 ,  H03M13/27 ,  H03M13/353 ,  H03M13/356 ,  H03M13/6312 ,  H04L1/0045 ,  H04L1/0057 ,  H04L1/0071

    Abstract: The present invention concerns a method of coding information symbols according to a code defined on a Galois field Fq, where q is an integer greater than 2 and equal to a power of a prime number, and of length n=p(q−1), where p>1. This coding is designed so that there exists a corresponding decoding method, also disclosed by the invention, in which the correction of transmission errors essentially comes down to the correction of errors in p words of length (q−1) coded according to Reed-Solomon. The invention is particularly advantageous when, through a suitable choice of parameters, the code according to the invention is an algebraic geometric code: in this case, it is possible to correct the transmission errors by the method already mentioned and/or by a conventional method which is less economical but has a higher performance.

    Abstract translation: 本发明涉及一种根据在伽罗瓦域Fq上定义的代码对信息符号进行编码的方法，其中q是大于2且等于质数的幂的整数，并且长度为n = p（q-1） ，其中p> 1。 该编码被设计成使得存在本发明也公开的对应的解码方法，其中传输错误的校正基本上归结于根据Reed-Solomon编码的长度（q-1）的p个字的错误的校正 。 当通过合适的参数选择，根据本发明的代码是代数几何代码时，本发明是特别有利的：在这种情况下，可以通过已经提及的方法和/或通过常规方法来校正传输错误 这是较不经济但具有较高的性能。

    Algebraic geometric code adapted to error bursts
    59.
    发明授权
    Algebraic geometric code adapted to error bursts 失效
    适用于错误突发的代数几何代码

    公开(公告)号：US07464323B2

    公开(公告)日：2008-12-09

    申请号：US10746144

    申请日：2003-12-29

    Applicant: Philippe Piret ,  Frédéric Lehobey ,  Philippe Le Bars ,  Frédérique Ehrmann-Patin

    Inventor： Philippe Piret ,  Frédéric Lehobey ,  Philippe Le Bars ,  Frédérique Ehrmann-Patin

    IPC: H03M13/00

    CPC classification number: H03M13/132 ,  H03M13/17

    Abstract: The present invention concerns channel codes particularly well adapted to transmission in channels in which errors tend to occur in bursts. Moreover, the codes according to one embodiment of the invention using an algebraic geometric curve are easy to decode and have a relatively high minimum distance. The invention also relates to the corresponding encoding and decoding methods, as well as the devices and apparatuses adapted to implement those methods. Application is in particular to mass storage, and to systems of communication by OFDM.

    Abstract translation: 本发明涉及特别适用于其中在突发中倾向于发生错误的信道中的传输的信道码。 此外，根据使用代数几何曲线的本发明的一个实施例的代码易于解码并且具有相对较高的最小距离。 本发明还涉及相应的编码和解码方法以及适于实现这些方法的装置和装置。 应用特别是大容量存储，以及通过OFDM的通信系统。

    Information encoding by shortened Reed-Solomon codes
    60.
    发明授权
    Information encoding by shortened Reed-Solomon codes 失效
    通过缩短Reed-Solomon码的信息编码

    公开(公告)号：US07398456B2

    公开(公告)日：2008-07-08

    申请号：US10565280

    申请日：2004-07-21

    Applicant: Philippe Piret ,  Philippe Le Bars ,  Frederic Lehobey

    Inventor： Philippe Piret ,  Philippe Le Bars ,  Frederic Lehobey

    IPC: H03M13/00

    CPC classification number: H03M13/159 ,  H03M13/1515 ,  H03M13/1535 ,  H03M13/155

    Abstract: The present invention concerns an encoding method in which encoding is performed of any information word a of length k in the form of a word ν belonging to a Reed-Solomon code C of dimension k′ and length n′ (with n′−k′=n−k) such that the components of ν′ situated in (n′−n) arbitrary predetermined positions be systematically equal to respective predetermined constants (for example, all zero). The possibility then exists of deleting those components of fixed value to obtain a word ν of length n belonging to a code C, which thus constitutes a code that is shortened with respect to code C. The invention also relates to devices and apparatuses adapted to implement the encoding method. The invention may be used for encoding by means of an algebraic geometric code, when such encoding may be implemented by encoding by means of a plurality of shortened Reed-Solomon codes.

    Abstract translation: 本发明涉及一种编码方法，其中以属于尺寸k'和长度n'（n'-k'）的Reed-Solomon码C的单词nu的形式的任何长度为k的信息字a执行编码， = nk），使得位于（n'-n）任意预定位置的nu'的分量系统地等于相应的预定常数（例如，全零）。 然后存在删除固定值的那些分量的可能性以获得属于代码C的长度为n的字nu，这样构成相对于代码C被缩短的代码。本发明还涉及适于实现的设备和装置 编码方法。 本发明可以用于通过代数几何码的编码，当这种编码可以通过借助于多个缩短的里德 - 所罗门码的编码来实现时。

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