MinT - Information on Result #941404

Information on Result #941404

Linear OOA(8¹⁶⁵, 139, F₈, 2, 85) (dual of [(139, 2), 113, 86]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵⁶, 65, F₈, 2, 42) (dual of [(65, 2), 74, 43]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,87P) [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(8¹⁰⁹, 74, F₈, 2, 85) (dual of [(74, 2), 39, 86]-NRT-code), using
- constructionÂ X applied to AG(2;F,42P) âŠ‚ AG(2;F,52P) [i] based on
  1. linear OOA(8⁹⁹, 64, F₈, 2, 85) (dual of [(64, 2), 29, 86]-NRT-code), using algebraic-geometric NRT-code AG(2;F,42P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁸⁹, 64, F₈, 2, 75) (dual of [(64, 2), 39, 76]-NRT-code), using algebraic-geometric NRT-code AG(2;F,52P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8¹⁰, 10, F₈, 2, 9) (dual of [(10, 2), 10, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8¹⁰, 14, F₈, 2, 9) (dual of [(14, 2), 18, 10]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,18P) [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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