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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi BAREKENG: Jurnal Ilmu Matematika dan Terapan
Hidayat, Ardi Nur
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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PERSYMMETRIC MATRIX AND ITS APPLICATION IN CODING THEORY Hidayat, Ardi Nur; Krisnawati, Vira Hari; Alghofari, Abdul Rouf
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2831-2842

Abstract

A persymmetric matrix is a square matrix that is symmetric concerning its antidiagonal. This article discusses some characteristics of a persymmetric matrix and its application in coding theory. A persymmetric matrix is used to form a generator matrix of binary reversible self-dual codes. A binary reversible self-dual code is a self-dual code whose reverse element is contained in the code. The methodology involves the implementation of flip transpose and column reversal to ensure the generator matrix satisfies both self-duality and reversibility. We begin with small-sized persymmetric matrices (e.g., 2×2 and 3×3) to extend the construction of the larger matrices. Combining a self-dual code and a reversible self-dual code of shorter length, and embedding persymmetric blocks, we construct new binary reversible self-dual codes of longer length. The novelty of this research lies in developing a new construction method for binary reversible self-dual codes derived directly from self-dual codes in the standard form, which has not been explicitly addressed in previous studies.
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 Abdul Rouf Alghofari Krisnawati, Vira Hari