40 research outputs found
Generalized Hamming weights of affine cartesian codes
In this article, we give the answer to the following question: Given a field
, finite subsets of , and linearly
independent polynomials of total
degree at most . What is the maximal number of common zeros
can have in ? For , the
finite field with elements, answering this question is equivalent to
determining the generalized Hamming weights of the so-called affine Cartesian
codes. Seen in this light, our work is a generalization of the work of
Heijnen--Pellikaan for Reed--Muller codes to the significantly larger class of
affine Cartesian codes.Comment: 12 Page
Binomial vanishing ideals
In this paper we characterize, in algebraic and geometric terms, when a
graded vanishing ideal is generated by binomials over any field K