MinT - Information on Result #2927950

Information on Result #2927950

Linear OOA(2²³⁹, 79, F₂, 6, 89) (dual of [(79, 6), 235, 90]-NRT-code), using 2¹ times duplication based on linear OOA(2²³⁸, 79, F₂, 6, 89) (dual of [(79, 6), 236, 90]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁸³, 33, F₂, 6, 44) (dual of [(33, 6), 115, 45]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(6;F,153P) [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(2¹⁵⁵, 46, F₂, 6, 89) (dual of [(46, 6), 121, 90]-NRT-code), using
  - constructionÂ X applied to AG(6;F,27P) âŠ‚ AG(6;F,29P) [i] based on
    1. linear OOA(2¹⁴³, 42, F₂, 6, 89) (dual of [(42, 6), 109, 90]-NRT-code), using algebraic-geometric NRT-code AG(6;F,27P) 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]
    2. linear OOA(2¹³¹, 42, F₂, 6, 77) (dual of [(42, 6), 121, 78]-NRT-code), using algebraic-geometric NRT-code AG(6;F,29P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42 (see above)
    3. linear OOA(2¹², 4, F₂, 6, 11) (dual of [(4, 6), 12, 12]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(2¹², 5, F₂, 5, 11) (dual of [(5, 5), 13, 12]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(5;F,13P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, 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.