MinT - Information on Result #1049097

Information on Result #1049097

Linear OOA(4²³⁹, 165, F₄, 3, 83) (dual of [(165, 3), 256, 84]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁸³, 61, F₄, 3, 41) (dual of [(61, 3), 100, 42]-NRT-code), using
- constructionÂ X applied to AG(3;F,123P) âŠ‚ AG(3;F,132P) [i] based on
  1. linear OOA(4⁷⁴, 55, F₄, 3, 41) (dual of [(55, 3), 91, 42]-NRT-code), using algebraic-geometric NRT-code AG(3;F,123P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. linear OOA(4⁶⁵, 55, F₄, 3, 32) (dual of [(55, 3), 100, 33]-NRT-code), using algebraic-geometric NRT-code AG(3;F,132P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
  3. linear OOA(4⁹, 6, F₄, 3, 8) (dual of [(6, 3), 9, 9]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4⁹, 9, F₄, 3, 8) (dual of [(9, 3), 18, 9]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,18P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]
linear OOA(4¹⁵⁶, 104, F₄, 3, 83) (dual of [(104, 3), 156, 84]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,228P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
  - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

Mode: Constructive and linear.

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