9 papers
Construction of a Family of Quantum Codes Using Sub-exceding Functions via the Hypergraph Product and the Generalized Shor Construction
Luc Rabefihavanana, Harinaivo Andriatahiny, Randriamiarampanahy Ferdinand
In this paper, we introduce a new family of stabilizer quantum LDPC codes derived from the classical linear codes and , defined via sub-exceding functions. In previo…
Error correcting codes from sub-exceeding fonction
Luc Rabefihavanana, Harinaivo Andriatahiny, Toussaint Rabeherimanana
In this paper, we present error-correcting codes which are the results of our research on the sub-exceeding functions. For a short and medium distance data transmission (wifi netwo…
A decoding algorithm for binary linear codes using Groebner bases
Harinaivo Andriatahiny, Jean Jacques Ferdinand Randriamiarampanahy, Toussaint Joseph Rabeherimanana
It has been discovered that linear codes may be described by binomial ideals. This makes it possible to study linear codes by commutative algebra and algebraic geometry methods. In…
Decoding binary Reed-Muller codes via Groebner bases
Harinaivo Andriatahiny, Jean Jacques Ferdinand Randriamiarampanahy, Toussaint Joseph Rabeherimanana
The binary Reed-Muller codes can be characterized as the radical powers of a modular algebra. We use the Groebner bases to decode these codes.
Generalized Reed-Muller codes over Galois rings
Harinaivo Andriatahiny, Desiré Arsène Ratahirinjatovo, Sanni José Andrianalisefa
Recently, Bhaintwal and Wasan studied the Generalized Reed-Muller codes over the prime power integer residue ring. In this paper, we give a generalization of these codes to General…
Standard Bases for Linear Codes over Prime Fields
Jean Jacques Ferdinand Randriamiarampanahy, Harinaivo Andriatahiny, Toussaint Joseph Rabeherimanana
It is known that a linear code can be represented by a binomial ideal. In this paper, we give standard bases for the ideals in a localization of the multivariate polynomial ring in…
New descriptions of the weighted Reed-Muller codes and the homogeneous Reed-Muller codes
Harinaivo Andriatahiny, Vololona Harinoro Rakotomalala
We give a description of the weighted Reed-Muller codes over a prime field in a modular algebra. A description of the homogeneous Reed-Muller codes in the same ambient space is pre…
The Generalized Reed-Muller codes in a modular group algebra
Harinaivo Andriatahiny, Vololona Harinoro Rakotomalala
First we study some properties of the modular group algebra where is the additive group of a Galois ring of characteristic and is…
The Generalized Reed-Muller codes and the radical powers of a modular algebra
Harinaivo Andriatahiny
First, a new proof of Berman and Charpin's characterization of the Reed-Muller codes over the binary field or over an arbitrary prime field is presented. These codes are considered…