MinT - Information on Result #1167592

Information on Result #1167592

Linear OOA(2¹⁶³, 38, F₂, 8, 51) (dual of [(38, 8), 141, 52]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁶³, 76, F₂, 4, 51) (dual of [(76, 4), 141, 52]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2³¹, 10, F₂, 4, 25) (dual of [(10, 4), 9, 26]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,14P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹³², 66, F₂, 4, 51) (dual of [(66, 4), 132, 52]-NRT-code), using
  - extracting embedded OOA [i] based on digital (81, 132, 66)-net over F₂, using
    - trace code for nets [i] based on digital (15, 66, 33)-net over F₄, using
      - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, 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.