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On the Schur Product of Vector Spaces over Finite Fields

Koster, C. J. (2012) On the Schur Product of Vector Spaces over Finite Fields. Bachelor's Thesis, Mathematics.

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Abstract

In this thesis we consider the vector space of all n-tuples over finite fields. We will investigate the Schur product, also known as entry-wise multiplication, of its linear subspaces, which is equal to the span of the Schur product over all pairs of vectors of a subspace. The number of d-dimensional linear subspaces will be counted, certain properties of the Schur product will be shown and the Schur product of cyclic codes will also be investigated. The main goal is to find good bounds on the number of subspaces for which the Schur product is equal to the total space. This will then be compared to the total number of subspaces as either the dimension of the vector space or the number of elements of the base field tend to infinity.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:49
Last Modified: 15 Feb 2018 07:49
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/10327

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