MinT - Information on Result #909639

Information on Result #909639

Linear OOA(4²⁴⁰, 123, F₄, 2, 181) (dual of [(123, 2), 6, 182]-NRT-code), using juxtaposition based on

linear OOA(4¹⁶, 11, F₄, 2, 13) (dual of [(11, 2), 6, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁶, 14, F₄, 2, 13) (dual of [(14, 2), 12, 14]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,14P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4²¹⁸, 112, F₄, 2, 167) (dual of [(112, 2), 6, 168]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(4¹⁰⁶, 56, F₄, 2, 83) (dual of [(56, 2), 6, 84]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14 (see above)
    2. linear OOA(4²⁷, 14, F₄, 2, 27) (dual of [(14, 2), 1, 28]-NRT-code), using
      - dual of repetition NRT-code with length 14 [i]
    3. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code) (see above)

Mode: Constructive and linear.

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