New Bounds for Linear Codes of Covering Radius 2

نویسندگان

  • Daniele Bartoli
  • Alexander A. Davydov
  • Massimo Giulietti
  • Stefano Marcugini
  • Fernanda Pambianco
چکیده

The length function lq(r,R) is the smallest length of a q-ary linear code of covering radius R and codimension r. New upper bounds on lq(r, 2) are obtained for odd r ≥ 3. In particular, using the one-to-one correspondence between linear codes of covering radius 2 and saturating sets in the projective planes over finite fields, we prove that

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تاریخ انتشار 2017