2018; Physical and Mathematical Sciences, 52(1 (245): 8–11
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ON THE MINIMAL COSET COVERINGS OF THE SET OF SINGULAR AND OF THE SET OF NONSINGULAR MATRICES

Ashot Minasya*

Received: 2025-02-04 · Published: 2018-04-16

© 2018 The Author(s) and the original publisher.

CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ON THE MINIMAL COSET COVERINGS OF THE SET OF SINGULAR AND OF THE SET OF NONSINGULAR MATRICES
Author
Ashot Minasya
Published
2018-04-16
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2018.52.1.008

Abstract

It is determined minimum number of cosets over linear subspaces in Fq necessary to cover following two sets of A(n×n) matrices. For one of the set of matrices detA=0 and for the other set detA≠0. It is proved that for singular matrices this number is equal to 1+q+q2+…+qn−1 and for the nonsingular matrices it is equal to (qn−1)(qn−q)(qn−q2)⋯(qn−qn−1)/q(n2).
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