MinT - Information on Result #1009808

Information on Result #1009808

Linear OOA(2¹⁸⁴, 78, F₂, 3, 61) (dual of [(78, 3), 50, 62]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁷⁴, 42, F₂, 3, 30) (dual of [(42, 3), 52, 31]-NRT-code), using
- extracting embedded OOA [i] based on digital (44, 74, 42)-net over F₂, using
  - trace code for nets [i] based on digital (7, 37, 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(2¹¹⁰, 39, F₂, 3, 61) (dual of [(39, 3), 7, 62]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹¹⁰, 42, F₂, 3, 61) (dual of [(42, 3), 16, 62]-NRT-code), using
  - strength reduction [i] based on linear OOA(2¹¹⁰, 42, F₂, 3, 65) (dual of [(42, 3), 16, 66]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(16¹⁰, 14, F₁₆, 10) (dual of [14, 4, 11]-code or 14-arc in PG(9,16)), using
        discarding factors / shortening the dual code based on linear OA(16¹⁰, 16, F₁₆, 10) (dual of [16, 6, 11]-code or 16-arc in PG(9,16)), using
        Reedâ€“Solomon code RS(6,16) [i]
      2. linear OOA(2⁵, 3, F₂, 3, 5) (dual of [(3, 3), 4, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;4,2) [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.