Paper Info
Title
On the next-to-minimal weight of affine cartesian codes.
Abstract
In this paper we determine many values of the second least weight of codewords, also known as the next-to-minimal Hamming weight, for a type of affine variety codes, obtained by evaluating polynomials of degree up to d on the points of a cartesian product of n subsets of a finite field F q . Such codes firstly appeared in a work by O. Geil and C. Thomsen (see 12) as a special case of the so-called weighted Reed-Muller codes, and later appeared independently in a work by H. López, C. Rentería-Marquez and R. Villarreal (see 16) named as affine cartesian codes. Our work extends, to affine cartesian codes, the results obtained by Rolland in 17 for generalized Reed-Muller codes.
Year
DOI
Venue
2017
10.1016/j.ffa.2016.11.005
Finite Fields and Their Applications
Keywords
Field
DocType
1T71,14G50,94B60,13P10
Affine transformation,Hamming code,Discrete mathematics,Combinatorics,Algebra,Affine coordinate system,Cartesian product,Block code,Linear code,Reed–Muller code,Affine hull,Mathematics
Journal
Volume
Issue
ISSN
44
C
1071-5797
Citations 
PageRank 
References 
1
0.40
6
Authors
2
Name
Order
Citations
PageRank
Cícero Carvalho1487.81
Victor G. L. Neumann262.68