MinT - Information on Result #909520

Information on Result #909520

Linear OOA(4²³⁴, 121, F₄, 2, 167) (dual of [(121, 2), 8, 168]-NRT-code), using juxtaposition based on

linear OOA(4¹⁸, 13, F₄, 2, 15) (dual of [(13, 2), 8, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁸, 14, F₄, 2, 15) (dual of [(14, 2), 10, 16]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,12P) [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(4²⁰⁸, 108, F₄, 2, 151) (dual of [(108, 2), 8, 152]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4⁴⁷, 27, F₄, 2, 37) (dual of [(27, 2), 7, 38]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,16P) [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, 50) (dual of [(27, 2), 1, 51]-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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