The Dynamics of Group Codes: Dual Abelian Group Codes and Systems

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dc.creatorForney Jr., G. David
dc.creatorTrott, Mitchell D.
dc.date2004-08-16
dc.date.accessioned2026-07-07T08:17:42Z
dc.date.available2026-07-07T08:17:42Z
dc.descriptionFundamental results concerning the dynamics of abelian group codes (behaviors) and their duals are developed. Duals of sequence spaces over locally compact abelian groups may be defined via Pontryagin duality; dual group codes are orthogonal subgroups of dual sequence spaces. The dual of a complete code or system is finite, and the dual of a Laurent code or system is (anti-)Laurent. If C and C^\perp are dual codes, then the state spaces of C act as the character groups of the state spaces of C^\perp. The controllability properties of C are the observability properties of C^\perp. In particular, C is (strongly) controllable if and only if C^\perp is (strongly) observable, and the controller memory of C is the observer memory of C^\perp. The controller granules of C act as the character groups of the observer granules of C^\perp. Examples of minimal observer-form encoder and syndrome-former constructions are given. Finally, every observer granule of C is an "end-around" controller granule of C.
dc.description30 pages, 11 figures. To appear in IEEE Trans. Inform. Theory, 2004
dc.identifierhttps://arxiv.org/abs/cs/0408038
dc.identifierhttp://arxiv.org/abs/cs/0408038
dc.identifierIEEE Trans. Inform. Theory, vol. 50, pp. 2935-2965, Dec. 2004.
dc.identifierdoi:10.1109/TIT.2004.838340
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134182
dc.subjectInformation Theory
dc.subjectE.4; H.1.1
dc.titleThe Dynamics of Group Codes: Dual Abelian Group Codes and Systems
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