Construction of the Annihilator of a Linear Recurring Sequence over Finite Module with the help of the Berlekamp-Massey Algorithm

V. L. Kurakin

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 476-483 from Springer

Abstract: Abstract Let M be a finite left module over a finite ring R with identity, u be a linear recurring sequence over M. In the previous paper of the author [1] an algorithm was stated which finds a minimal polynomial μ(x) ∈ R[x] of a finite sequence u( $$u(\overline {0,l - 1} )$$ ). In this paper we show that for sufficiently large l the polynomials developed in this algorithm form a generating system for the annihilator An(u) ⊑ R[x] of the sequence u. This result can also be applied to a sequence over a right module, over a bimodule, and over a ring R.

Date: 2000
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DOI: 10.1007/978-3-662-04166-6_45

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