Paper Info
Title
Affine Cartesian codes with complementary duals.
Abstract
A linear code C with the property that C∩C⊥={0} is said to be a linear complementary dual, or LCD, code. In this paper, we consider generalized affine Cartesian codes which are LCD. Generalized affine Cartesian codes arise naturally as the duals of affine Cartesian codes in the same way that generalized Reed–Solomon codes arise as duals of Reed–Solomon codes. Generalized affine Cartesian codes are evaluation codes constructed by evaluating multivariate polynomials of bounded degree at points in an m-dimensional Cartesian set over a finite field K and scaling the coordinates. The LCD property depends on the scalars used. Because Reed–Solomon codes are a special case, we obtain a characterization of those generalized Reed–Solomon codes which are LCD along with the more general result for generalized affine Cartesian codes. These results are independent of the characteristic of the underlying field.
Year
DOI
Venue
2018
10.1016/j.ffa.2019.01.004
Finite Fields and Their Applications
Keywords
Field
DocType
11T71,94B27,14G50
Affine transformation,Discrete mathematics,Finite field,Scalar (mathematics),Dual polyhedron,Linear code,Scaling,Mathematics,Cartesian coordinate system,Bounded function
Journal
Volume
ISSN
Citations 
57
1071-5797
0
PageRank 
References 
Authors
0.34
8
3
Name
Order
Citations
PageRank
Hiram H. López1204.81
Felice Manganiello2165.09
Gretchen L. Matthews38113.47