MinT - Information on Result #941444

Information on Result #941444

Linear OOA(8¹⁶⁹, 140, F₈, 2, 87) (dual of [(140, 2), 111, 88]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵⁷, 65, F₈, 2, 43) (dual of [(65, 2), 73, 44]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,86P) [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(8¹¹², 75, F₈, 2, 87) (dual of [(75, 2), 38, 88]-NRT-code), using
- constructionÂ X applied to AG(2;F,40P) âŠ‚ AG(2;F,51P) [i] based on
  1. linear OOA(8¹⁰¹, 64, F₈, 2, 87) (dual of [(64, 2), 27, 88]-NRT-code), using algebraic-geometric NRT-code AG(2;F,40P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁹⁰, 64, F₈, 2, 76) (dual of [(64, 2), 38, 77]-NRT-code), using algebraic-geometric NRT-code AG(2;F,51P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8¹¹, 11, F₈, 2, 10) (dual of [(11, 2), 11, 11]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8¹¹, 14, F₈, 2, 10) (dual of [(14, 2), 17, 11]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,17P) [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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