MinT - Information on Result #1027527

Information on Result #1027527

Linear OOA(4²⁵⁷, 87, F₄, 3, 222) (dual of [(87, 3), 4, 223]-NRT-code), using juxtaposition based on

linear OOA(4²³, 9, F₄, 3, 22) (dual of [(9, 3), 4, 23]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,4P) [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(4²³⁰, 78, F₄, 3, 199) (dual of [(78, 3), 4, 200]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4²⁰, 8, F₄, 3, 19) (dual of [(8, 3), 4, 20]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4²⁰, 9, F₄, 3, 19) (dual of [(9, 3), 7, 20]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9 (see above)
  2. linear OOA(4²⁰⁶, 70, F₄, 3, 179) (dual of [(70, 3), 4, 180]-NRT-code), using
    - repeating each code word 5 times [i] based on linear OOA(4³⁸, 14, F₄, 3, 35) (dual of [(14, 3), 4, 36]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,6P) [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.

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