MinT - Information on Result #909511

Information on Result #909511

Linear OOA(4¹⁷⁸, 93, F₄, 2, 125) (dual of [(93, 2), 8, 126]-NRT-code), using juxtaposition based on

linear OOA(4¹⁰, 9, F₄, 2, 9) (dual of [(9, 2), 8, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,8P) [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(4¹⁶⁰, 84, F₄, 2, 115) (dual of [(84, 2), 8, 116]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4³⁵, 21, F₄, 2, 28) (dual of [(21, 2), 7, 29]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,13P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4⁴¹, 21, F₄, 2, 38) (dual of [(21, 2), 1, 39]-NRT-code), using
    - strength reduction [i] based on linear OOA(4⁴¹, 21, F₄, 2, 41) (dual of [(21, 2), 1, 42]-NRT-code), using
      - dual of repetition NRT-code with length 21 [i]
  3. linear OOA(4⁴², 21, F₄, 2, 42) (dual of [(21, 2), 0, 43]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4⁴², 21, F₄, 2, 42) (dual of [(21, 2), 0, 43]-NRT-code) (see above)

Mode: Constructive and linear.

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