MinT - Information on Result #909566

Information on Result #909566

Linear OOA(4²²⁵, 116, F₄, 2, 164) (dual of [(116, 2), 7, 165]-NRT-code), using juxtaposition based on

linear OOA(4⁹, 8, F₄, 2, 8) (dual of [(8, 2), 7, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁹, 9, F₄, 2, 8) (dual of [(9, 2), 9, 9]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,9P) [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(4²⁰⁹, 108, F₄, 2, 155) (dual of [(108, 2), 7, 156]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4⁴⁸, 27, F₄, 2, 38) (dual of [(27, 2), 6, 39]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,15P) [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, 51) (dual of [(27, 2), 1, 52]-NRT-code), using
    - strength reduction [i] based on 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]
  4. linear OOA(4⁵⁴, 27, F₄, 2, 54) (dual of [(27, 2), 0, 55]-NRT-code) (see above)

Mode: Constructive and linear.

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