MinT - Information on Result #1011355

Information on Result #1011355

Linear OOA(3¹⁷⁶, 72, F₃, 3, 86) (dual of [(72, 3), 40, 87]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁹, 36, F₃, 3, 43) (dual of [(36, 3), 39, 44]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,64P) [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using
  - an explicitly constructive algebraic function field [i]
- algebraic-geometric NRT-code AG(3;F,32P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
linear OOA(3¹⁰⁷, 36, F₃, 3, 86) (dual of [(36, 3), 1, 87]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁰⁷, 37, F₃, 3, 86) (dual of [(37, 3), 4, 87]-NRT-code), using
  - strength reduction [i] based on linear OOA(3¹⁰⁷, 37, F₃, 3, 87) (dual of [(37, 3), 4, 88]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3⁸, 4, F₃, 3, 8) (dual of [(4, 3), 4, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;4,3) [i]
      2. linear OOA(3⁹⁵, 33, F₃, 3, 78) (dual of [(33, 3), 4, 79]-NRT-code), using
        strength reduction [i] based on linear OOA(3⁹⁵, 33, F₃, 3, 79) (dual of [(33, 3), 4, 80]-NRT-code), using
        juxtaposition [i] based on
        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]
        linear OOA(3⁷⁴, 26, F₃, 3, 62) (dual of [(26, 3), 4, 63]-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(3⁵³, 19, F₃, 3, 45) (dual of [(19, 3), 4, 46]-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(3³², 12, F₃, 3, 28) (dual of [(12, 3), 4, 29]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
        an explicitly constructive algebraic function field [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.