MinT - Information on Result #1129439

Information on Result #1129439

Linear OOA(2²²⁰, 78, F₂, 5, 78) (dual of [(78, 5), 170, 79]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁸⁸, 36, F₂, 5, 39) (dual of [(36, 5), 92, 40]-NRT-code), using
- constructionÂ X applied to AG(5;F,120P) âŠ‚ AG(5;F,130P) [i] based on
  1. linear OOA(2⁷⁸, 32, F₂, 5, 39) (dual of [(32, 5), 82, 40]-NRT-code), using algebraic-geometric NRT-code AG(5;F,120P) [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(2⁶⁸, 32, F₂, 5, 29) (dual of [(32, 5), 92, 30]-NRT-code), using algebraic-geometric NRT-code AG(5;F,130P) [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]
linear OOA(2¹³², 42, F₂, 5, 78) (dual of [(42, 5), 78, 79]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(5;F,131P) [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.

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