MinT - Information on Result #909473

Information on Result #909473

Linear OOA(4²¹², 111, F₄, 2, 145) (dual of [(111, 2), 10, 146]-NRT-code), using juxtaposition based on

linear OOA(4⁵⁰, 30, F₄, 2, 37) (dual of [(30, 2), 10, 38]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,22P) [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
  - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
linear OOA(4¹⁵², 81, F₄, 2, 107) (dual of [(81, 2), 10, 108]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4⁴⁵, 27, F₄, 2, 35) (dual of [(27, 2), 9, 36]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,18P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4⁵³, 27, F₄, 2, 53) (dual of [(27, 2), 1, 54]-NRT-code), using
    - dual of repetition NRT-code with length 27 [i]
  3. linear OOA(4⁵⁴, 27, F₄, 2, 54) (dual of [(27, 2), 0, 55]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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