MinT - Information on Result #1025164

Information on Result #1025164

Linear OOA(2²⁰⁹, 74, F₂, 3, 109) (dual of [(74, 3), 13, 110]-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(2¹⁰⁷, 40, F₂, 3, 59) (dual of [(40, 3), 13, 60]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴⁸, 20, F₂, 3, 29) (dual of [(20, 3), 12, 30]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,30P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2⁵⁹, 20, F₂, 3, 59) (dual of [(20, 3), 1, 60]-NRT-code), using
    - dual of repetition NRT-code with length 20 [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.