Paper Info
Title
Enumeration of linear transformation shift registers
Abstract
We consider the problem of counting the number of linear transformation shift registers (TSRs) of a given order over a finite field. We derive explicit formulae for the number of irreducible TSRs of order two. An interesting connection between TSRs and self-reciprocal polynomials is outlined. We use this connection and our results on TSRs to deduce a theorem of Carlitz on the number of self-reciprocal irreducible monic polynomials of a given degree over a finite field.
Year
DOI
Venue
2015
10.1007/s10623-013-9913-5
Designs, Codes and Cryptography
Keywords
Field
DocType
Block companion matrix,Linear feedback shift register (LFSR),Self-reciprocal polynomial,Splitting subspace,Transformation shift register (TSR),12E05,15A33,11T71
Discrete mathematics,Combinatorics,Finite field,Shift register,Explicit formulae,Polynomial,Enumeration,Monic polynomial,Linear map,Mathematics
Journal
Volume
Issue
ISSN
75
2
Designs, Codes and Cryptography, Vol. 75, No. 2 (2015), pp. 301-314
Citations 
PageRank 
References 
4
0.46
11
Authors
1
Name
Order
Citations
PageRank
Samrith Ram1203.52