Generalised Multi-sequence Shift-Register Synthesis using Module Minimisation

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We show how to solve a generalised version of the Multi-sequence Linear Feedback Shift-Register (MLFSR) problem using minimisation of free modules over F[x]. We show how two existing algorithms for minimising such modules run particularly fast on these instances. Furthermore, we show how one of them can be made even faster for our use. With our modelling of the problem, classical algebraic results tremendously simplify arguing about the algorithms. For the non-generalised MLFSR, these algorithms are as fast as what is currently known. We then use our generalised MLFSR to give a new fast decoding algorithm for Reed Solomon codes.
Original languageEnglish
Title of host publication2013 IEEE International Symposium on Information Theory Proceedings (ISIT)
Publication date2013
ISBN (Print)978-1-4799-0446-4
Publication statusPublished - 2013
EventIEEE International Symposium on Information Theory (ISIT 2013) - Istanbul, Turkey
Duration: 7 Jul 201312 Jul 2013


ConferenceIEEE International Symposium on Information Theory (ISIT 2013)
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