MinT - Information on Result #941387

Information on Result #941387

Linear OOA(8¹⁶⁸, 143, F₈, 2, 84) (dual of [(143, 2), 118, 85]-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(8¹¹², 78, F₈, 2, 84) (dual of [(78, 2), 44, 85]-NRT-code), using
- constructionÂ X applied to AG(2;F,43P) âŠ‚ AG(2;F,57P) [i] based on
  1. linear OOA(8⁹⁸, 64, F₈, 2, 84) (dual of [(64, 2), 30, 85]-NRT-code), using algebraic-geometric NRT-code AG(2;F,43P) [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(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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