State representations of convolutional codes over a finite ring

Napp, Diego; Pinto, Raquel; Rocha, Conceição

doi:10.1016/j.laa.2021.12.006

Cited by 1 publication

(1 citation statement)

References 39 publications

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“…In particular, the algebraic study of linear systems in the state-space approach [3] deals with linear systems defned on algebras and modules over a commutative ring [4,5]. Tis approach has been used recently in the feld of convolutional codes [6][7][8][9][10]. Convolutional codes are in fact error-correcting codes over a fnite feld F defned as vector subspaces of F(z) n , where F (z) is the feld of rationals which are realized as linear control systems over F .…”

Section: Introductionmentioning

confidence: 99%

Natural Factorization of Linear Control Systems through Parallel Gathering of Simple Systems

Carriegos

2023

Journal of Mathematics

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Linear systems over vector spaces and feedback morphisms form an additive category taking into account the parallel gathering of linear systems. This additive category has a minimal exact structure and thus a notion of simple systems as those systems have no subsystems apart from zero and themselves. The so-called single-input systems are proven to be exactly the simple systems in the category of reachable systems over vector spaces. The category is also proven to be semisimple in objects because every reachable linear system is decomposed in a finite parallel gathering of simple systems. Hence, decomposition result is fulfilled for linear systems and feedback morphisms, but category of reachable linear systems is not abelian semisimple because it is not balanced and hence fails to be abelian. Finally, it is conjectured that the category of linear systems and feedback actions is in fact semiabelian; some threads to find the result and consequences are also given.

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Section: Introductionmentioning

confidence: 99%

Natural Factorization of Linear Control Systems through Parallel Gathering of Simple Systems

Carriegos

2023

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

State representations of convolutional codes over a finite ring

Cited by 1 publication

References 39 publications

Natural Factorization of Linear Control Systems through Parallel Gathering of Simple Systems

Natural Factorization of Linear Control Systems through Parallel Gathering of Simple Systems

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