4 citations · 11 across the 9 of their papers we have counts for
15 papers
Integer Reasoning Modulo Different Constants in SMT
Elizaveta Pertseva, Alex Ozdemir, Shankara Pailoor +4
This paper presents a new refutation procedure for multimodular systems of integer constraints that commonly arise when verifying cryptographic protocols. These systems, involving…
Iterative constructions of irreducible polynomials from isogenies
Alp Bassa, Gaetan Bisson, Roger Oyono
Let be a rational fraction and let be a polynomial over a finite field. Consider the transform . In certain cases, the polynomials ,…
The Only Complex 4-Net Is the Hesse Configuration
Alp Bassa, Ali Ulas Ozgur Kisisel
It has been conjectured that the only nets realizable in are 3-nets and the Hesse configuration (up to isomorphism). We prove this conjecture.
The R-transform as a power map and its generalisations to higher degree
Alp Bassa, Ricardo Menares
We give iterative constructions for irreducible polynomials over F_q of degree nt^r for all nonnegative integers r, starting from irreducible polynomials of degree n. The iterative…
Enumeration of a special class of irreducible polynomials in characteristic 2
Alp Bassa, Ricardo Menares
A-polynomials were introduced by Meyn and play an important role in the iterative construction of high degree self-reciprocal irreducible polynomials over the field F_2, since they…
On the Deuring Polynomial for Drinfeld Modules in Legendre Form
Alp Bassa, Peter Beelen
We study a family of -Drinfeld modules, which is a natural analog of Legendre elliptic curves. We then find a surprising recurrence giving the corresponding D…
Good recursive towers over prime fields exist
Alp Bassa, Christophe Ritzenthaler
We give a construction and equations for good recursive towers over any finite field with and .
Self-Dual Codes better than the Gilbert--Varshamov bound
Alp Bassa, Henning Stichtenoth
We show that every self-orthogonal code over of length can be extended to a self-dual code, if there exists self-dual codes of length . Using a family of Galoi…
A modular interpretation of various cubic towers
Nurdagül Anbar, Alp Bassa, Peter Beelen
In this article we give a Drinfeld modular interpretation for various towers of function fields meeting Zink's bound.
A complete characterization of Galois subfields of the generalized Giulietti--Korchmáros function field
Nurdagül Anbar, Alp Bassa, Peter Beelen
We give a complete characterization of all Galois subfields of the generalized Giulietti--Korchmáros function fields $\mathcal C_n / \fqn$ for . Calculating the genera of t…
Good families of Drinfeld modular curves
Alp Bassa, Peter Beelen, Nhut Nguyen
In this paper we investigate examples of good and optimal Drinfeld modular towers of function fields. Surprisingly, the optimality of these towers has not been investigated in full…
Galois Towers over Non-prime Finite Fields
Alp Bassa, Peter Beelen, Arnaldo Garcia +1
In this paper we construct Galois towers with good asymptotic properties over any non-prime finite field ; i.e., we construct sequences of function fields $\mathc…
A closed form expression for the Drinfeld modular polynomial
Alp Bassa, Peter Beelen
In this paper we give a closed form expression for the Drinfeld modular polynomial for arbitrary and prove a conjecture of Schweizer. A new…
Towers of Function Fields over Non-prime Finite Fields
Alp Bassa, Peter Beelen, Arnaldo Garcia +1
Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bound…
Explicit equations for Drinfeld modular towers
Alp Bassa, Peter Beelen
Elaborating on ideas of Elkies, we show how recursive equations for towers of Drinfeld modular curves for can be read of directly from t…