On Multisequences and their extensions
This work addresses theoretical problems in sequence analysis and linear algebra, with applications in designing linear feedback shift registers, but it appears incremental as it builds on existing multisequence theory.
The paper tackles the problem of determining the dimension of multisequences and their extensions, resulting in a method to count multisequences with maximum dimension and applications to counting LFSR configurations and Hankel matrices.
In this paper we deal with the dimension of multisequences and related properties. For a given multisequence W and an m tuple of positive integers R, we define the R extension of W. Further we count the number of multisequences W whose R extensions have maximum dimension and give an algorithm to derive such multisequences. We then go on to use this theory to count the number of Linear Feedback Shift Register(LFSR) configurations with multi input multi output delay blocks for any given primitive characteristic polynomial and also to design such LFSRs. Further, we use the result on multisequences to count the number of Hankel matrices of any given dimension.