MinT - Information on Result #941365

Information on Result #941365

Linear OOA(8¹⁶⁵, 142, F₈, 2, 83) (dual of [(142, 2), 119, 84]-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, 77, F₈, 2, 83) (dual of [(77, 2), 44, 84]-NRT-code), using
- constructionÂ X applied to AG(2;F,44P) âŠ‚ AG(2;F,57P) [i] based on
  1. linear OOA(8⁹⁷, 64, F₈, 2, 83) (dual of [(64, 2), 31, 84]-NRT-code), using algebraic-geometric NRT-code AG(2;F,44P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁸⁴, 64, F₈, 2, 70) (dual of [(64, 2), 44, 71]-NRT-code), using algebraic-geometric NRT-code AG(2;F,57P) [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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