Counting functions and expected values for the lattice profile at n

Authors:
Gerhard Dorfer;Wilfried Meidl;Arne Winterhof
Affiliations:
Department of Algebra and Computational Mathematics, Vienna University of Technology, Wiedner Hauptstr.8-10/118, Vienna A-1040, Austria;Temasek Laboratories, National University of Singapore, 5 Sports Drive 2, Singapore 117508, Singapore;Temasek Laboratories, National University of Singapore, 5 Sports Drive 2, Singapore 117508, Singapore and Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Scie ...
Venue:
Finite Fields and Their Applications
Year:
2004

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Abstract

Recently, Dorfer and Winterhof introduced and analyzed a lattice test for sequences of length n over a finite field. We determine the number of sequences @h of length n with given largest dimension S"n(@h)=S for passing this test. From this result we derive an exact formula for the expected value of S"n(@h). For the binary case we characterize the (infinite) sequences @h with maximal possible S"n(@h) for all n.