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UID:5530@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20131212T110000
DTEND;TZID=Europe/Paris:20131212T120000
DTSTAMP:20241030T094049Z
URL:https://www.i2m.univ-amu.fr/evenements/enumeration-of-block-companion-
 singer-cycles/
SUMMARY:Samrith Ram (...): Enumeration of block companion Singer cycles
DESCRIPTION:Samrith Ram: We discuss the enumeration of nonsingular matrices
  over a finite field that are block companion and whose order is the maxim
 um possible in the corresponding general linear group. The problem is esse
 ntially equivalent to counting the number of so-called primitive 'word-ori
 ented' linear feedback shift registers($\\sigma$-LFSR). A connection with 
 an older problem of Niederreiter about the number of splitting subspaces o
 f a given dimension is outlined. A special case of the problem is equivale
 nt to finding the probability that a pair of polynomials of given degree w
 ith coefficients in a finite field is coprime. We also discuss the enumera
 tion of a subclass of $\\sigma$-LFSRs called Transformation Shift Register
 s (TSR).\n\nSamrith Ram\, IIT Bombay
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
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DTSTART:20131027T020000
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