44 citations · 57 across the 28 of their papers we have counts for
8 papers · 1 filter
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…
The Möbius function of for any prime
Martino Borello, Francesca Dalla Volta, Giovanni Zini
Let be the simple group , where is a prime number. For any subgroup of , we compute the Möbius function of in the subgroup lattice of . To t…
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…