MinT - Information on Result #1089407

Information on Result #1089407

Linear OOA(2¹⁹⁷, 64, F₂, 4, 84) (dual of [(64, 4), 59, 85]-NRT-code), using constructionÂ X applied to AG(4;F,79P) âŠ‚ AG(4;F,112P) based on

linear OOA(2¹³⁸, 41, F₂, 4, 84) (dual of [(41, 4), 26, 85]-NRT-code), using algebraic-geometric NRT-code AG(4;F,79P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
- an explicitly constructive algebraic function field [i]
linear OOA(2¹⁰⁵, 41, F₂, 4, 51) (dual of [(41, 4), 59, 52]-NRT-code), using algebraic-geometric NRT-code AG(4;F,112P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42 (see above)
linear OOA(2⁵⁹, 23, F₂, 4, 32) (dual of [(23, 4), 33, 33]-NRT-code), using
- constructionÂ X applied to AG(4;F,43P) âŠ‚ AG(4;F,51P) [i] based on
  1. linear OOA(2⁵¹, 19, F₂, 4, 32) (dual of [(19, 4), 25, 33]-NRT-code), using algebraic-geometric NRT-code AG(4;F,43P) [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(2⁴³, 19, F₂, 4, 24) (dual of [(19, 4), 33, 25]-NRT-code), using algebraic-geometric NRT-code AG(4;F,51P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20 (see above)
  3. linear OOA(2⁸, 4, F₂, 4, 7) (dual of [(4, 4), 8, 8]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2⁸, 5, F₂, 3, 7) (dual of [(5, 3), 7, 8]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,7P) [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.

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