MinT - Information on Result #1049116

Information on Result #1049116

Linear OOA(4²⁴⁶, 166, F₄, 3, 86) (dual of [(166, 3), 252, 87]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁸⁷, 62, F₄, 3, 43) (dual of [(62, 3), 99, 44]-NRT-code), using
- constructionÂ X applied to AG(3;F,121P) âŠ‚ AG(3;F,132P) [i] based on
  1. linear OOA(4⁷⁶, 55, F₄, 3, 43) (dual of [(55, 3), 89, 44]-NRT-code), using algebraic-geometric NRT-code AG(3;F,121P) [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(4¹¹, 7, F₄, 3, 10) (dual of [(7, 3), 10, 11]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹¹, 9, F₄, 3, 10) (dual of [(9, 3), 16, 11]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,16P) [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(4¹⁵⁹, 104, F₄, 3, 86) (dual of [(104, 3), 153, 87]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,225P) [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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