MinT - Information on Result #1120557

Information on Result #1120557

Linear OOA(2²⁴⁷, 54, F₂, 5, 155) (dual of [(54, 5), 23, 156]-NRT-code), using juxtaposition based on

linear OOA(2⁹², 23, F₂, 5, 61) (dual of [(23, 5), 23, 62]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁹², 24, F₂, 5, 61) (dual of [(24, 5), 28, 62]-NRT-code), using
  - constructionÂ X applied to AG(5;F,38P) âŠ‚ AG(5;F,48P) [i] based on
    1. linear OOA(2⁸², 20, F₂, 5, 61) (dual of [(20, 5), 18, 62]-NRT-code), using algebraic-geometric NRT-code AG(5;F,38P) [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]
    2. linear OOA(2⁷², 20, F₂, 5, 51) (dual of [(20, 5), 28, 52]-NRT-code), using algebraic-geometric NRT-code AG(5;F,48P) [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21 (see above)
    3. linear OOA(2¹⁰, 4, F₂, 5, 9) (dual of [(4, 5), 10, 10]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(2¹⁰, 5, F₂, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,10P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]
linear OOA(2¹³², 31, F₂, 5, 93) (dual of [(31, 5), 23, 94]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹³², 32, F₂, 5, 93) (dual of [(32, 5), 28, 94]-NRT-code), using
  - algebraic-geometric NRT-code AG(5;F,66P) [i] based on function field F/F₂ with g(F) = 39 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.