44 citations · 57 across the 28 of their papers we have counts for
22 papers · 1 filter
A -analogue of the rational normal curve and linearized Reed-Solomon codes
Valentina Astore, Martino Borello, Alain Couvreur +1
The relationship between linear codes in the Hamming metric and projective algebraic varieties has led to deep interactions between coding theory and algebraic geometry, with class…
On the existence of linear rank-metric intersecting codes
Martino Borello, Olga Polverino, Ferdinando Zullo
Intersecting codes are a classical object in coding theory whose rank-metric analogue has recently been introduced. Although the definition formally parallels the Hamming-metric ca…
A geometric invariant of linear rank-metric codes
Valentina Astore, Martino Borello, Marco Calderini +1
Rank-metric codes have been a central topic in coding theory due to their theoretical and practical significance, with applications in network coding, distributed storage, crisscro…
Twisted skew -codes
Angelot Behajaina, Martino Borello, Javier de la Cruz +1
In this paper we investigate left ideals as codes in twisted skew group rings. The considered rings, which are often algebras over a finite field, allows us to detect many of the w…
Left ideal LRPC codes and a ROLLO-type cryptosystem based on group algebras
Martino Borello, Paolo Santonastaso, Ferdinando Zullo
In this paper we introduce left ideal low-rank parity-check codes by using group algebras and we finally use them to extend ROLLO-I KEM.
Dihedral codes with prescribed minimum distance
Martino Borello, Abdelillah Jamous
Dihedral codes, particular cases of quasi-cyclic codes, have a nice algebraic structure which allows to store them efficiently. In this paper, we investigate it and prove some lowe…
A geometric characterization of minimal codes and their asymptotic performance
Gianira Nicoletta Alfarano, Martino Borello, Alessandro Neri
In this paper, we give a geometric characterization of minimal linear codes. In particular, we relate minimal linear codes to cutting blocking sets, introduced in a recent paper by…
On the algebraic structure of quasi group codes
Martino Borello, Wolfgang Willems
In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, a…
A Note on Linear Complementary Pairs of Group Codes
Martino Borello, Javier de la Cruz, Wolfgang Willems
We give a short and elementary proof of the fact that for a linear complementary pair , where and are -sided ideals in a group algebra, is uniquely determined…
Minimal linear codes arising from blocking sets
Matteo Bonini, Martino Borello
Minimal linear codes are algebraic objects which gained interest in the last twenty years, due to their link with Massey's secret sharing schemes. In this context, Ashikhmin and Ba…
Asymptotic performance of metacyclic codes
Martino Borello, Pieter Moree, Patrick Solé
A finite group with a cyclic normal subgroup N such that G/N is cyclic is said to be metacyclic. A code over a finite field F is a metacyclic code if it is a left ideal in the grou…
Group codes over fields are asymptotically good
Martino Borello, Wolfgang Willems
Group codes are right or left ideals in a group algebra of a finite group over a finite field. Following ideas of Bazzi and Mitter on group codes over the binary field, we prove th…
On checkable codes in group algebras
Martino Borello, Javier de la Cruz, Wolfgang Willems
We classify, in terms of the structure of the finite group G, all group algebras KG for which all right ideals are right annihilators of principal left ideals. This means in the la…
The Concatenated Structure of Quasi-Abelian Codes
Martino Borello, Cem Güneri, Elif Saçıkara +1
The decomposition of a quasi-abelian code into shorter linear codes over larger alphabets was given in (Jitman, Ling, (2015)), extending the analogous Chinese remainder decompositi…
Symmetries of weight enumerators and applications to Reed-Muller codes
Martino Borello, Olivier Mila
Gleason's 1970 theorem on weight enumerators of self-dual codes has played a crucial role for research in coding theory during the last four decades. Plenty of generalizations have…
Some new results on the self-dual [120,60,24] code
Martino Borello, Javier de la Cruz
The existence of an extremal self-dual binary linear code of length 120 is a long-standing open problem. We continue the investigation of its automorphism group, proving that autom…
On the Stabilizer of Weight Enumerators of Linear Codes
Martino Borello, Olivier Mila
This paper investigates the relation between linear codes and the stabilizer in of their weight enumerators. We prove a result on the finiteness of stabili…
On the automorphism groups of binary linear codes
Martino Borello
Let C be a binary linear code and suppose that its automorphism group contains a non trivial subgroup G. What can we say about C knowing G? In this paper we collect some answers to…
The automorphism group of a self-dual [72,36,16] code is not an elementary abelian group of order 8
Martino Borello
The existence of an extremal self-dual binary linear code C of length 72 is a long-standing open problem. We continue the investigation of its automorphism group: looking at the co…
The automorphism group of a self-dual [72,36,16] code does not contain S_3, A_4, or D_8
Martino Borello, Francesca Dalla Volta, Gabriele Nebe
A computer calculation with Magma shows that there is no extremal self-dual binary code C of length 72, whose automorphism group contains the symmetric group of degree 3, the alter…
Automorphism of order 2p in binary self-dual extremal codes of length a multiple of 24
Martino Borello, Wolfgang Willems
Let C be a binary self-dual code with an automorphism g of order 2p, where p is an odd prime, such that g^p is a fixed point free involution. If C is extremal of length a multiple…
The Automorphism Group of an Extremal [72,36,16] Code does not contain elements of order 6
Martino Borello
The existence of an extremal code of length 72 is a long-standing open problem. Let C be a putative extremal code of length 72 and suppose that C has an automorphism g of order 6.…