MinT - Information on Result #2761049

Information on Result #2761049

Linear OOA(2¹⁴², 37, F₂, 4, 99) (dual of [(37, 4), 6, 100]-NRT-code), using strength reduction based on linear OOA(2¹⁴², 37, F₂, 4, 104) (dual of [(37, 4), 6, 105]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹⁸, 6, F₂, 4, 16) (dual of [(6, 4), 6, 17]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,7P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹¹⁸, 31, F₂, 4, 87) (dual of [(31, 4), 6, 88]-NRT-code), using
  - strength reduction [i] based on linear OOA(2¹¹⁸, 31, F₂, 4, 88) (dual of [(31, 4), 6, 89]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2²², 7, F₂, 4, 19) (dual of [(7, 4), 6, 20]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,8P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(2⁹⁰, 24, F₂, 4, 68) (dual of [(24, 4), 6, 69]-NRT-code), using
        repeating each code word 3 times [i] based on linear OOA(2²⁶, 8, F₂, 4, 22) (dual of [(8, 4), 6, 23]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,9P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, 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.