5 citations · 7 across the 6 of their papers we have counts for
6 papers
On the third weight of generalized Reed-Muller codes
Elodie Leducq
In this paper, we study the third weight of generalized Reed-Muller codes. We prove under some restrictive condition that the third weight of generalized Reed-Muller codes depends…
Second weight codewords of generalized Reed-Muller codes
Elodie Leducq
In this paper we give the second weight codewords of the generalized Reed-Muller code of order r and length .
On the covering radius of first order generalized Reed-Muller codes
Elodie Leducq
We generalize to any q a theorem about covering radius of linear codes proved by Helleseth, Klove and Mykkelvit. Then we determine the covering radius of first order generalized Re…
A proof of two conjectures on APN functions
Elodie Leducq
Dobbertin, Mills, Müller, Pott and Willems conjecture that two families of power mapping are families of APN functions. Here we prove those two conjectures.
Functions which are PN on infiitely many extensions of Fp, p odd
Elodie Leducq
Let be an odd prime number. We prove that for , is perfectly nonlinear over for infinitely many if and only if is of the form $…
A new proof of Delsarte, Goethals and Mac Williams theorem on minimal weight codewords of generalized Reed-Muller code
Elodie Leducq
We give a new proof of Delsarte, Goethals and Mac williams theorem on minimal weight codewords of generalized Reed-Muller codes published in 1970. To prove this theorem, we conside…