MinT - Information on Result #1020598

Information on Result #1020598

Linear OOA(3²²⁷, 84, F₃, 3, 137) (dual of [(84, 3), 25, 138]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁶⁰, 28, F₃, 3, 45) (dual of [(28, 3), 24, 46]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,38P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3⁸³, 28, F₃, 3, 68) (dual of [(28, 3), 1, 69]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁸³, 29, F₃, 3, 68) (dual of [(29, 3), 4, 69]-NRT-code), using
  - strength reduction [i] based on linear OOA(3⁸³, 29, F₃, 3, 69) (dual of [(29, 3), 4, 70]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(3⁶², 22, F₃, 3, 52) (dual of [(22, 3), 4, 53]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code) (see above)
        linear OOA(3⁴¹, 15, F₃, 3, 35) (dual of [(15, 3), 4, 36]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code) (see above)
        linear OOA(3²⁰, 8, F₃, 3, 18) (dual of [(8, 3), 4, 19]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,5P) [i] based on function field F/F₃ with g(F) = 2 and N(F) ≥ 8, using
        an explicitly constructive algebraic function field [i]
linear OOA(3⁸⁴, 28, F₃, 3, 84) (dual of [(28, 3), 0, 85]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.