6 papers
Construction of Multicyclic Codes of Arbitrary Dimension via Idempotents: A Unified Combinatorial-Algebraic Approach
Jean Charles Ramanandraibe, Ramamonjy Andriamifidisoa
We propose a unified method to construct multicyclic codes of arbitrary dimension over . The approach relies on -dimensional primitive idempotents defined as t…
DM-RSA: An Extension of RSA with Dual Modulus
Andriamifidisoa Ramamonjy, Rufine Marius Lalasoa
We introduce DM-RSA (Dual Modulus RSA), a variant of the RSA cryptosystem that employs two distinct moduli symmetrically to enhance security. By leveraging the Chinese Remainder Th…
Finding a Generator Matrix of a Multidimensional Cyclic Code
R. Andriamifidisoa, R. M. Lalasoa, T. J. Rabeherimanana
We generalize Sepasdar's method for finding a generator matrix of two-dimensional cyclic codes to find an independent subset of a general multicyclic code, which may form a basis o…
A Dynamical System-based Key Equation for Decoding One-Point Algebraic-Geometry Codes
Ramamonjy Andriamifidisoa, Rufine Marius Lalasoa, Toussaint Joseph Rabeherimanana
A closer look at linear recurring sequences allowed us to define the multiplication of a univariate polynomial and a sequence, viewed as a power series with another variable, resul…
Duality of Discrete Topological Vector Spaces
Ramamonjy Andriamifidisoa
For a field $\ef$, the discrete topological vector spaces over $\ \ef$ are essentially of the form $\ef^α$ where is an ordinal. With additional appropriate properties, they are…
Discrete linear Algebraic Dynamical Systems
Ramamonjy Andriamifidisoa, Juanito Andrianjanahary
The vector space of the multi-indexed sequences over a field and the vector space of the sequences with finite support are dual to each other, with respect to a \textit{scalar prod…