RT info:eu-repo/semantics/article
T1 High dimensional affine codes whose square has a designed minimum distance
A1 García Marco, Ignacio
A1 Márquez Corbella, Irene
A1 Ruano Benito, Diego
AB Given a linear code C, its square code C(2) is the span of all component-wise products of two elements of C. Motivated by applications in multi-party computation, our purpose with this work is to answer the following question: which families of affine variety codes have simultaneously high dimension k(C) and high minimum distance of C(2), d(C(2))? More precisely, given a designed minimum distance d we compute an affine variety code C such that d(C(2))≥d and the dimension of C is high. The best constructions we propose mostly come from hyperbolic codes. Nevertheless, for small values of d, they come from weighted Reed–Muller codes
PB Springer
SN 0925-1022
YR 2020
FD 2020
LK http://uvadoc.uva.es/handle/10324/45998
UL http://uvadoc.uva.es/handle/10324/45998
LA eng
NO I. García-Marco, Irene Márquez-Corbella, Diego Ruano: High dimensional affine codes whose square has a designed minimum distance. Designs, Codes and Cryptography. Volume 88, pages 1653-1672 (2020)
NO Producción Científica
DS UVaDOC
RD 29-abr-2024