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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Electronic Journal of Graph Theory and Applications (EJGTA) Jurnal Mahasiswa Matematika Journal of Natural A Science and Technology Indonesia BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Matematika UNAND Indonesian Journal of Mathematics and Applications
Abdul Rouf Alghofari
Jurusan Matematika, Fakultas MIPA, Universitas Brawijaya
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Transportation Other

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Reversible Self-Dual Codes over Finite Field Hidayat, Ardi Nur; Krisnawati, Vira Hari; Alghofari, Abdul Rouf
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.29116

Abstract

Reversible self-dual code is a linear code which combine the properties from self-dual code and reversible code. Previous research shows that reversible self-dual codes have only been developed over field of order 2 and order 4. In this article, we construct reversible self-dual code over any finite field of order F_q ,  with natural number q=2.  We first examine and prove some of fundamental properties of reversible self-dual code over . After a thorough analysis these, we obtain a new generator matrix of reversible self-dual code.  A new generator matrix is derived from existing self-dual and reversible self-dual code over . It will be shown that a new reversible self-dual over  can be constructs from one and more existing code by specific algebraic methods. Furthermore, using this construction, we determine the minimum distance of reversible self-dual code and ensuring its optimal performance in various applications.
Co-Authors Diari Indriati Diari Indriati Fadilatul I., Nur Hidayat, Ardi Nur Hidayat, Noor Krisnawati, Vira Hari Kwardiniya Andawaningtyas Mohamad Muslikh Noor Hidayat, Noor NUR HAMID Pramudita, Riski S Slamin Sa'adatul Fitri shalsabilla, Az Zahra Slamin Syaiful Anam Syarifatul Azaliyah, Syarifatul Wijaya, Ongky Denny Wijayanti, Dian Eka