WEIGHTS OF THE Fq-FORMS OF 2-STEP SPLITTING TRIVECTORS OF RANK 8 OVER A FINITE FIELD

dc.contributor.authorMohamed Anouar RAKDI
dc.date.accessioned2021-07-27T09:19:53Z
dc.date.available2021-07-27T09:19:53Z
dc.date.issued2021
dc.description.abstractGrassmann codes are linear codes associated with the Grassmann variety G(`;m) of `-dimensional subspaces of an m dimensional vector space Fmq : They were studied by Nogin for general q: These codes are conveniently described using the correspondence between non-degenerate [n; k]q linear codes on one hand and non-degenerate [n; k] projective systems on the other hand. A non-degenerate [n; k] projective system is simply a collection of n points in projective space Pk􀀀1 satisfying the condition that no hyperplane of Pk􀀀1 contains all the n points under consideration. In this paper we will determine the weight of linear codes C(3; 8) associated with Grassmann varieties G(3; 8) over an arbitrary finite field Fq. We use a formula for the weight of a codeword of C(3; 8), in terms of the cardinalities certain varieties associated with alternating trilinear forms on F8q : For m = 6 and 7; the weight spectrum of C(3;m) associated with G(3;m); have been fully determined by Kaipa K.V, Pillai H.K and Nogin Y. A classification of trivectors depends essentially on the dimension n of the base space. For n 8 there exist only finitely many trivector classes under the action of the general linear group GL(n): The methods of Galois cohomology can be used to determine the classes of nondegenerate trivectors which split into multiple classes when going from F to F: This program is partially determined by Noui L and Midoune N and the classification of trilinear alternating forms on a vector space of dimension 8 over a finite field Fq of characteristic other than 2 and 3 was solved by Noui L and Midoune N. We describe the Fq-forms of 2-step splitting trivectors of rank 8, where char Fq 6= 3: This fact we use to determine the weight of the Fq-formsen_US
dc.identifier.urihttp://dspace.univ-msila.dz:8080//xmlui/handle/123456789/25201
dc.publisherUniversité de M'silaen_US
dc.subjectwords and phrases: trivector, Grassmannian, weighten_US
dc.titleWEIGHTS OF THE Fq-FORMS OF 2-STEP SPLITTING TRIVECTORS OF RANK 8 OVER A FINITE FIELDen_US
dc.typeArticleen_US

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