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h2i-EXPONENTS OF SHIFT REGISTER TRANSFORMATIONS NONLINEARITY DIPGRAPHS [О h2i-ЭКСПОНЕНТАХ ОРГРАФОВ НЕЛИНЕЙНОСТИ РЕГИСТРОВЫХ ПРЕОБРАЗОВАНИЙ]

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dc.contributor.authorFomichev, V. M.
dc.contributor.authorBobrov, V. M.
dc.date.accessioned2024-12-25T07:52:23Z
dc.date.available2024-12-25T07:52:23Z
dc.date.issued2022
dc.description.abstractThe matrix-graph approach is used to estimate sets of essential and non-linear variables of coordinate functions of the vector space transformations product. Estimates are obtained by multiplying binary mixing matrices or digraphs of multiplied transformations in the case of the set of essential variables, or by multiplying ternary nonlinearity matrices or corresponding nonlinearity digraphs with the arcs marked by numbers from the set 0, 1, 2. For powers of a given transformation the non-trivial estimates domain is limited by the mixing matrix (digraph) exponent in the case of the essential variables and by the nonlinearity matrix (digraph) h2i-exponent in the case of the nonlinear variables. Let f(x0, . . ., xn-1) be the feedback function of shift register, D = d0, . . ., dm be the set of its essential variables (registers extraction points), 1 andlt; m 6 n, 0 = d0 andlt; d1 andlt; . . . andlt; dm andlt; n, E = e0, . . ., el be the set of its nonlinear variables (registers nonlinear extraction points), 1 andlt; l 6 n, e0 andlt; e1 andlt; . . . andlt; em andlt; n, and shift register transformation nonlinearity digraph G be h2i-primitive. Then h2iexponent of G is not greater than F(L)+1+n+∆f, where F(L) is a Frobenius number of the set L of the lengths of all digraph simple circuits, (Equation presented), where d(u) is the greatest number of D such that d(u) 6 u, 0 6 u andlt; n; e(u) is the greatest number of E such that e(u) 6 u, e0 6 u andlt; n; S0(n) = S1(n) = ∅, if dm = n - 1; S0(n) = n
dc.format.extentС. 77-87
dc.identifier.citationFomichev, V. M. h2i-EXPONENTS OF SHIFT REGISTER TRANSFORMATIONS NONLINEARITY DIPGRAPHS [О h2i-ЭКСПОНЕНТАХ ОРГРАФОВ НЕЛИНЕЙНОСТИ РЕГИСТРОВЫХ ПРЕОБРАЗОВАНИЙ] / Fomichev, V.M., Bobrov, V.M. // Prikladnaya Diskretnaya Matematika. - 2022. - № 55. - P. 77-87. - 10.17223/20710410/55/5
dc.identifier.doi10.17223/20710410/55/5
dc.identifier.urihttps://www.doi.org/10.17223/20710410/55/5
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85136261391&origin=resultslist
dc.identifier.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000780031400005
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/27355
dc.relation.ispartofPrikladnaya Diskretnaya Matematika
dc.titleh2i-EXPONENTS OF SHIFT REGISTER TRANSFORMATIONS NONLINEARITY DIPGRAPHS [О h2i-ЭКСПОНЕНТАХ ОРГРАФОВ НЕЛИНЕЙНОСТИ РЕГИСТРОВЫХ ПРЕОБРАЗОВАНИЙ]
dc.typeArticle
dspace.entity.typePublication
oaire.citation.issue55
relation.isOrgUnitOfPublication010157d0-1f75-46b2-ab5b-712e3424b4f5
relation.isOrgUnitOfPublication.latestForDiscovery010157d0-1f75-46b2-ab5b-712e3424b4f5
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