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A note on the minimal polynomial of the product of linear recurring sequences
Date
1999-08-06
Author
Cakcak, E
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Let F be a field of nonzero characteristic, with its algebraic closure, F. For positive integers a, b, let J(a, b) be the set of integers k, such that (x - 1)k is the minimal polynomial of the termwise product of linear recurring sequences sigma and tau in F ($) over bar, with minimal polynomials (x - 1)(a) and (x - 1)(b) respectively. This set plays a crucial role in the determination of the product of linear recurring sequences with arbitrary minimal polynomials. Here, we give an explicit formula to determine some of the elements of J(a, b), in the case of characteristic 2. We also give some clues for the extension to arbitrary characteristic. The method given here has produced a family of matrices which are themselves interesting.
Subject Keywords
Finite field
,
Linear complexity
,
Algebraic closure
,
Minimal polynomial
,
Block diagonal matrix
URI
https://hdl.handle.net/11511/63786
Collections
Department of Mathematics, Conference / Seminar
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E. Cakcak, “A note on the minimal polynomial of the product of linear recurring sequences,” 1999, p. 57, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63786.