MinT - Information on Result #1027446

Information on Result #1027446

Linear OOA(4¹⁷², 59, F₄, 3, 145) (dual of [(59, 3), 5, 146]-NRT-code), using juxtaposition based on

linear OOA(4²², 9, F₄, 3, 21) (dual of [(9, 3), 5, 22]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,5P) [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(4¹⁴⁵, 50, F₄, 3, 123) (dual of [(50, 3), 5, 124]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4¹⁹, 8, F₄, 3, 18) (dual of [(8, 3), 5, 19]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹⁹, 9, F₄, 3, 18) (dual of [(9, 3), 8, 19]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,8P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9 (see above)
  2. linear OOA(4¹²¹, 42, F₄, 3, 104) (dual of [(42, 3), 5, 105]-NRT-code), using
    - repeating each code word 3 times [i] based on linear OOA(4³⁷, 14, F₄, 3, 34) (dual of [(14, 3), 5, 35]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result: