Random Generator of Orthogonal Matrices in Finite Fields

Lasha Ephremidze, Ilya Spitkovsky

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationAdvances in Information and Communication - Proceedings of the 2024 Future of Information and Communication Conference FICC
EditorsKohei Arai
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages11
ISBN (Print)9783031539626
StatePublished - 2024
EventFuture of Information and Communication Conference, FICC 2024 - Berlin, Germany
Duration: Apr 4 2024Apr 5 2024

Publication series

NameLecture Notes in Networks and Systems
Volume920 LNNS
ISSN (Print)2367-3370
ISSN (Electronic)2367-3389


ConferenceFuture of Information and Communication Conference, FICC 2024


  • Finite fields
  • Orthogonal matrices
  • Paraunitary filter banks

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications


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