MinT - Information on Result #2839875

Information on Result #2839875

Linear OOA(2¹²⁶, 26, F₂, 5, 101) (dual of [(26, 5), 4, 102]-NRT-code), using strength reduction based on linear OOA(2¹²⁶, 26, F₂, 5, 106) (dual of [(26, 5), 4, 107]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹⁶, 4, F₂, 5, 15) (dual of [(4, 5), 4, 16]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2¹⁶, 5, F₂, 5, 15) (dual of [(5, 5), 9, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(5;F,9P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹⁰⁶, 22, F₂, 5, 90) (dual of [(22, 5), 4, 91]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2¹⁶, 4, F₂, 5, 15) (dual of [(4, 5), 4, 16]-NRT-code) (see above)
    2. linear OOA(2⁸⁶, 18, F₂, 5, 74) (dual of [(18, 5), 4, 75]-NRT-code), using
      - repeating each code word 3 times [i] based on linear OOA(2²⁶, 6, F₂, 5, 24) (dual of [(6, 5), 4, 25]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(5;F,5P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, 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.