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

dc.contributor.author | Mohamed Anouar RAKDI | |

dc.date.accessioned | 2021-07-27T09:19:53Z | |

dc.date.available | 2021-07-27T09:19:53Z | |

dc.date.issued | 2021 | |

dc.description.abstract | Grassmann 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 Pk1 satisfying the condition that no hyperplane of Pk1 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-forms | en_US |

dc.identifier.uri | http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/25201 | |

dc.publisher | Université de M'sila | en_US |

dc.subject | words and phrases: trivector, Grassmannian, weight | en_US |

dc.title | WEIGHTS OF THE Fq-FORMS OF 2-STEP SPLITTING TRIVECTORS OF RANK 8 OVER A FINITE FIELD | en_US |

dc.type | Article | en_US |