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On the second Hamming weight of some Reed-Muller type codes

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 نشر من قبل Cicero Carvalho
 تاريخ النشر 2013
  مجال البحث الهندسة المعلوماتية
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 تأليف Cicero Carvalho




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We study affine cartesian codes, which are a Reed-Muller type of evaluation codes, where polynomials are evaluated at the cartesian product of n subsets of a finite field F_q. These codes appeared recently in a work by H. Lopez, C. Renteria-Marquez and R. Villareal and, in a generalized form, in a work by O. Geil and C. Thomsen. Using methods from Grobner basis theory we determine the second Hamming weight (also called next-to-minimal weight) for particular cases of affine cartesian codes and also some higher Hamming weights of this type of code.



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