MinT - Information on Result #1080659

Information on Result #1080659

Linear OOA(2²⁵⁷, 76, F₂, 4, 107) (dual of [(76, 4), 47, 108]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁰⁷, 42, F₂, 4, 53) (dual of [(42, 4), 61, 54]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,114P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]
- algebraic-geometric NRT-code AG(4;F,19P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
linear OOA(2¹⁵⁰, 38, F₂, 4, 107) (dual of [(38, 4), 2, 108]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁵⁰, 39, F₂, 4, 107) (dual of [(39, 4), 6, 108]-NRT-code), using
  - strength reduction [i] based on linear OOA(2¹⁵⁰, 39, F₂, 4, 112) (dual of [(39, 4), 6, 113]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2³⁰, 9, F₂, 4, 25) (dual of [(9, 4), 6, 26]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,10P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(2¹¹⁴, 30, F₂, 4, 86) (dual of [(30, 4), 6, 87]-NRT-code), using
        repeating each code word 3 times [i] based on linear OOA(2³⁴, 10, F₂, 4, 28) (dual of [(10, 4), 6, 29]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,11P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, 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.