MinT - Information on Result #1086481

Information on Result #1086481

Linear OOA(2¹⁹⁷, 55, F₂, 4, 107) (dual of [(55, 4), 23, 108]-NRT-code), using juxtaposition based on

linear OOA(2⁶⁹, 23, F₂, 4, 40) (dual of [(23, 4), 23, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁶⁹, 24, F₂, 4, 40) (dual of [(24, 4), 27, 41]-NRT-code), using
  - constructionÂ X applied to AG(4;F,35P) âŠ‚ AG(4;F,45P) [i] based on
    1. linear OOA(2⁵⁹, 19, F₂, 4, 40) (dual of [(19, 4), 17, 41]-NRT-code), using algebraic-geometric NRT-code AG(4;F,35P) [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(2⁴⁹, 19, F₂, 4, 30) (dual of [(19, 4), 27, 31]-NRT-code), using algebraic-geometric NRT-code AG(4;F,45P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20 (see above)
    3. 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(2¹⁰⁵, 32, F₂, 4, 66) (dual of [(32, 4), 23, 67]-NRT-code), using
- algebraic-geometric NRT-code AG(4;F,61P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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