8 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…