MinT - Information on Result #941344

Information on Result #941344

Linear OOA(8¹⁶⁵, 143, F₈, 2, 82) (dual of [(143, 2), 121, 83]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵⁵, 65, F₈, 2, 41) (dual of [(65, 2), 75, 42]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,88P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
  - the Suzuki function field over F₈ [i]
linear OOA(8¹¹⁰, 78, F₈, 2, 82) (dual of [(78, 2), 46, 83]-NRT-code), using
- constructionÂ X applied to AG(2;F,45P) âŠ‚ AG(2;F,59P) [i] based on
  1. linear OOA(8⁹⁶, 64, F₈, 2, 82) (dual of [(64, 2), 32, 83]-NRT-code), using algebraic-geometric NRT-code AG(2;F,45P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁸², 64, F₈, 2, 68) (dual of [(64, 2), 46, 69]-NRT-code), using algebraic-geometric NRT-code AG(2;F,59P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8¹⁴, 14, F₈, 2, 13) (dual of [(14, 2), 14, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,14P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

Mode: Constructive and linear.

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