High dimensional affine codes whose square has a designed minimum distance

被引：4

作者：

Garcia-Marco, Ignacio ^{[1
]}

Marquez-Corbella, Irene ^{[1
]}

Ruano, Diego ^{[2
]}

机构：

[1] Univ La Laguna, Dept Matemat Estadist & IO, Tenerife 38200, Spain

[2] Univ Valladolid, Math Res Inst, IMUVA, Valladolid 47011, Spain

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2020年 / 88卷 / 08期

关键词：

Affine variety codes; Multi-party computation; Square codes; Schur product of codes; Minkowski sum; Convex set; LINEAR CODES;

D O I：

10.1007/s10623-020-00764-5

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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.

引用

页码：1653 / 1672

页数：20