MinT - Information on Result #2846565

Information on Result #2846565

Linear OOA(2²³³, 78, F₂, 5, 86) (dual of [(78, 5), 157, 87]-NRT-code), using strength reduction based on linear OOA(2²³³, 78, F₂, 5, 87) (dual of [(78, 5), 157, 88]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁹², 36, F₂, 5, 43) (dual of [(36, 5), 88, 44]-NRT-code), using
  - constructionÂ X applied to AG(5;F,116P) âŠ‚ AG(5;F,126P) [i] based on
    1. linear OOA(2⁸², 32, F₂, 5, 43) (dual of [(32, 5), 78, 44]-NRT-code), using algebraic-geometric NRT-code AG(5;F,116P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
    2. linear OOA(2⁷², 32, F₂, 5, 33) (dual of [(32, 5), 88, 34]-NRT-code), using algebraic-geometric NRT-code AG(5;F,126P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33 (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]
2. linear OOA(2¹⁴¹, 42, F₂, 5, 87) (dual of [(42, 5), 69, 88]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,122P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, 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.