MinT - Information on Result #1123423

Information on Result #1123423

Linear OOA(2²⁵¹, 65, F₂, 5, 122) (dual of [(65, 5), 74, 123]-NRT-code), using constructionÂ X applied to AG(5;F,82P) âŠ‚ AG(5;F,127P) based on

linear OOA(2¹⁷⁶, 41, F₂, 5, 122) (dual of [(41, 5), 29, 123]-NRT-code), using algebraic-geometric NRT-code AG(5;F,82P) [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(2¹³¹, 41, F₂, 5, 77) (dual of [(41, 5), 74, 78]-NRT-code), using algebraic-geometric NRT-code AG(5;F,127P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42 (see above)
linear OOA(2⁷⁵, 24, F₂, 5, 44) (dual of [(24, 5), 45, 45]-NRT-code), using
- constructionÂ X applied to AG(5;F,55P) âŠ‚ AG(5;F,65P) [i] based on
  1. linear OOA(2⁶⁵, 20, F₂, 5, 44) (dual of [(20, 5), 35, 45]-NRT-code), using algebraic-geometric NRT-code AG(5;F,55P) [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]
  2. linear OOA(2⁵⁵, 20, F₂, 5, 34) (dual of [(20, 5), 45, 35]-NRT-code), using algebraic-geometric NRT-code AG(5;F,65P) [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21 (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]

Mode: Constructive and linear.

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