MinT - Information on Result #1009752

Information on Result #1009752

Linear OOA(2¹⁷³, 80, F₂, 3, 54) (dual of [(80, 3), 67, 55]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁸, 42, F₂, 3, 27) (dual of [(42, 3), 58, 28]-NRT-code), using
- extracting embedded OOA [i] based on digital (41, 68, 42)-net over F₂, using
  - trace code for nets [i] based on digital (7, 34, 21)-net over F₄, using
    - net from sequence [i] based on digital (7, 20)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
        an explicitly constructive algebraic function field [i]
linear OOA(2¹⁰⁵, 40, F₂, 3, 54) (dual of [(40, 3), 15, 55]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴⁶, 20, F₂, 3, 27) (dual of [(20, 3), 14, 28]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,32P) [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, 54) (dual of [(20, 3), 1, 55]-NRT-code), using
    - strength reduction [i] based on 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.