MinT - Information on Result #941322

Information on Result #941322

Linear OOA(8¹⁶², 142, F₈, 2, 81) (dual of [(142, 2), 122, 82]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵⁴, 65, F₈, 2, 40) (dual of [(65, 2), 76, 41]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,89P) [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(8¹⁰⁸, 77, F₈, 2, 81) (dual of [(77, 2), 46, 82]-NRT-code), using
- constructionÂ X applied to AG(2;F,46P) âŠ‚ AG(2;F,59P) [i] based on
  1. linear OOA(8⁹⁵, 64, F₈, 2, 81) (dual of [(64, 2), 33, 82]-NRT-code), using algebraic-geometric NRT-code AG(2;F,46P) [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(8¹³, 13, F₈, 2, 12) (dual of [(13, 2), 13, 13]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8¹³, 14, F₈, 2, 12) (dual of [(14, 2), 15, 13]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,15P) [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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