3 papers
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.
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…