MinT - Information on Result #2846670

Information on Result #2846670

Linear OOA(2²³⁴, 79, F₂, 5, 85) (dual of [(79, 5), 161, 86]-NRT-code), using strength reduction based on linear OOA(2²³⁴, 79, F₂, 5, 86) (dual of [(79, 5), 161, 87]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁸², 33, F₂, 5, 43) (dual of [(33, 5), 83, 44]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,121P) [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(2¹⁵², 46, F₂, 5, 86) (dual of [(46, 5), 78, 87]-NRT-code), using
  - constructionÂ X applied to AG(5;F,20P) âŠ‚ AG(5;F,22P) [i] based on
    1. linear OOA(2¹⁴³, 42, F₂, 5, 89) (dual of [(42, 5), 67, 90]-NRT-code), using algebraic-geometric NRT-code AG(5;F,20P) 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, 5, 77) (dual of [(42, 5), 79, 78]-NRT-code), using algebraic-geometric NRT-code AG(5;F,22P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42 (see above)
    3. linear OOA(2⁹, 4, F₂, 5, 8) (dual of [(4, 5), 11, 9]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(2⁹, 5, F₂, 4, 8) (dual of [(5, 4), 11, 9]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,11P) [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.