TY - GEN
T1 - Toward good families of codes from towers of surfaces
AU - Couvreur, Alain
AU - Lebacque, Philippe
AU - Perret, Marc
N1 - Publisher Copyright:
© 2021 American Mathematical Society.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be “liftable” under finite morphisms, paving the way toward the construction of good codes from towers of surfaces. In the same direction, we establish a criterion for a surface with a fixed finite set of closed points P to have an infinite tower of ℓ–étale covers in which P splits totally. We conclude by stating several open problems. In particular, we relate the existence of asymptotically good codes from general type surfaces with a very ample canonical class to the behaviour of their number of rational points with respect to their K2 and coherent Euler characteristic.
AB - We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be “liftable” under finite morphisms, paving the way toward the construction of good codes from towers of surfaces. In the same direction, we establish a criterion for a surface with a fixed finite set of closed points P to have an infinite tower of ℓ–étale covers in which P splits totally. We conclude by stating several open problems. In particular, we relate the existence of asymptotically good codes from general type surfaces with a very ample canonical class to the behaviour of their number of rational points with respect to their K2 and coherent Euler characteristic.
UR - https://www.scopus.com/pages/publications/85139033120
U2 - 10.1090/conm/770/15431
DO - 10.1090/conm/770/15431
M3 - Conference contribution
AN - SCOPUS:85139033120
SN - 9781470454265
T3 - Contemporary Mathematics
SP - 59
EP - 101
BT - Arithmetic, Geometry, Cryptography and Coding Theory - 17th International Conference Arithmetic, Geometry, Cryptography and Coding Theory, 2019
A2 - Ballet, Stéphane
A2 - Bisson, Gaetan
A2 - Bouw, Irene
PB - American Mathematical Society
T2 - 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory, AGC2T-17 2019
Y2 - 10 June 2019 through 14 June 2019
ER -