MinT - Information on Result #2905930

Information on Result #2905930

Linear OOA(2⁷⁵, 23, F₂, 6, 43) (dual of [(23, 6), 63, 44]-NRT-code), using strength reduction based on linear OOA(2⁷⁵, 23, F₂, 6, 44) (dual of [(23, 6), 63, 45]-NRT-code), using

constructionÂ X applied to AG(6;F,69P) âŠ‚ AG(6;F,81P) [i] based on
1. linear OOA(2⁶³, 19, F₂, 6, 44) (dual of [(19, 6), 51, 45]-NRT-code), using algebraic-geometric NRT-code AG(6;F,69P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(2⁵¹, 19, F₂, 6, 32) (dual of [(19, 6), 63, 33]-NRT-code), using algebraic-geometric NRT-code AG(6;F,81P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20 (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.