5 research outputs found

    Generalized Hamming weights of affine cartesian codes

    Get PDF
    In this article, we give the answer to the following question: Given a field F\mathbb{F}, finite subsets A1,…,AmA_1,\dots,A_m of F\mathbb{F}, and rr linearly independent polynomials f1,…,fr∈F[x1,…,xm]f_1,\dots,f_r \in \mathbb{F}[x_1,\dots,x_m] of total degree at most dd. What is the maximal number of common zeros f1,…,frf_1,\dots,f_r can have in A1×⋯×AmA_1 \times \cdots \times A_m? For F=Fq\mathbb{F}=\mathbb{F}_q, the finite field with qq 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

    More results on the number of zeros of multiplicity at least r

    No full text

    Topics on Reliable and Secure Communication using Rank-Metric and Classical Linear Codes

    Get PDF
    corecore