MinT - Information on Result #1011209

Information on Result #1011209

Linear OOA(3¹⁵³, 64, F₃, 3, 74) (dual of [(64, 3), 39, 75]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁵⁸, 32, F₃, 3, 37) (dual of [(32, 3), 38, 38]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,58P) [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3⁹⁵, 32, F₃, 3, 74) (dual of [(32, 3), 1, 75]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁹⁵, 34, F₃, 3, 74) (dual of [(34, 3), 7, 75]-NRT-code), using
  - constructionÂ X applied to AG(3;F,0P) âŠ‚ AG(3;F,21P) [i] based on
    1. linear OOA(3⁸⁰, 27, F₃, 3, 80) (dual of [(27, 3), 1, 81]-NRT-code), using algebraic-geometric NRT-code AG(3;F,0P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]
    2. linear OOA(3⁷⁴, 27, F₃, 3, 59) (dual of [(27, 3), 7, 60]-NRT-code), using algebraic-geometric NRT-code AG(3;F,21P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
    3. linear OOA(3¹⁵, 7, F₃, 3, 14) (dual of [(7, 3), 6, 15]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,6P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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