MinT - Information on Result #1049111

Information on Result #1049111

Linear OOA(4²⁴⁵, 167, F₄, 3, 85) (dual of [(167, 3), 256, 86]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁸⁷, 63, F₄, 3, 42) (dual of [(63, 3), 102, 43]-NRT-code), using
- constructionÂ X applied to AG(3;F,122P) âŠ‚ AG(3;F,134P) [i] based on
  1. linear OOA(4⁷⁵, 55, F₄, 3, 42) (dual of [(55, 3), 90, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,122P) [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(4⁶³, 55, F₄, 3, 30) (dual of [(55, 3), 102, 31]-NRT-code), using algebraic-geometric NRT-code AG(3;F,134P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
  3. linear OOA(4¹², 8, F₄, 3, 11) (dual of [(8, 3), 12, 12]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹², 9, F₄, 3, 11) (dual of [(9, 3), 15, 12]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,15P) [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(4¹⁵⁸, 104, F₄, 3, 85) (dual of [(104, 3), 154, 86]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,226P) [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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