MinT - Information on Result #1025165

Information on Result #1025165

Linear OOA(2²⁵⁷, 90, F₂, 3, 133) (dual of [(90, 3), 13, 134]-NRT-code), using juxtaposition based on

linear OOA(2⁸⁹, 34, F₂, 3, 49) (dual of [(34, 3), 13, 50]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2³⁹, 17, F₂, 3, 24) (dual of [(17, 3), 12, 25]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,26P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2⁵⁰, 17, F₂, 3, 49) (dual of [(17, 3), 1, 50]-NRT-code), using
    - strength reduction [i] based on linear OOA(2⁵⁰, 17, F₂, 3, 50) (dual of [(17, 3), 1, 51]-NRT-code), using
      - dual of repetition NRT-code with length 17 [i]
linear OOA(2¹⁵⁵, 56, F₂, 3, 83) (dual of [(56, 3), 13, 84]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁷², 28, F₂, 3, 41) (dual of [(28, 3), 12, 42]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2³¹, 14, F₂, 3, 20) (dual of [(14, 3), 11, 21]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,21P) [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(2⁴¹, 14, F₂, 3, 41) (dual of [(14, 3), 1, 42]-NRT-code), using
        dual of repetition NRT-code with length 14 [i]
  2. linear OOA(2⁸³, 28, F₂, 3, 83) (dual of [(28, 3), 1, 84]-NRT-code), using
    - dual of repetition NRT-code with length 28 [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.