TY - GEN
T1 - Random Generator of Orthogonal Matrices in Finite Fields
AU - Ephremidze, Lasha
AU - Spitkovsky, Ilya
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - We propose a superfast method for constructing orthogonal matrices M∈O(n,q) in finite fields GF(q). It can be used to construct n×n orthogonal matrices in Zp with very high values of n and p, and also orthogonal matrices with a certain circulant structure. Equally well one can construct paraunitary filter banks or wavelet matrices over finite fields. The construction mechanism is highly efficient, allowing for the complete screening and selection of an orthogonal matrix that meets specific constraints. For instance, one can generate a complete list of orthogonal matrices with given n and q=pm provided that the order of O(n,q) is not too large. Although the method is based on randomness, isolated cases of failure can be identified well in advance of the basic procedure’s start. The proposed procedures are based on the Janashia-Lagvilava method which was developed for an entirely different task, therefore, it may seem somewhat unexpected.
AB - We propose a superfast method for constructing orthogonal matrices M∈O(n,q) in finite fields GF(q). It can be used to construct n×n orthogonal matrices in Zp with very high values of n and p, and also orthogonal matrices with a certain circulant structure. Equally well one can construct paraunitary filter banks or wavelet matrices over finite fields. The construction mechanism is highly efficient, allowing for the complete screening and selection of an orthogonal matrix that meets specific constraints. For instance, one can generate a complete list of orthogonal matrices with given n and q=pm provided that the order of O(n,q) is not too large. Although the method is based on randomness, isolated cases of failure can be identified well in advance of the basic procedure’s start. The proposed procedures are based on the Janashia-Lagvilava method which was developed for an entirely different task, therefore, it may seem somewhat unexpected.
KW - Finite fields
KW - Orthogonal matrices
KW - Paraunitary filter banks
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U2 - 10.1007/978-3-031-53963-3_20
DO - 10.1007/978-3-031-53963-3_20
M3 - Conference contribution
AN - SCOPUS:85189293993
SN - 9783031539626
T3 - Lecture Notes in Networks and Systems
SP - 290
EP - 300
BT - Advances in Information and Communication - Proceedings of the 2024 Future of Information and Communication Conference FICC
A2 - Arai, Kohei
PB - Springer Science and Business Media Deutschland GmbH
T2 - Future of Information and Communication Conference, FICC 2024
Y2 - 4 April 2024 through 5 April 2024
ER -