MinT - Information on Result #909710

Information on Result #909710

Linear OOA(4¹⁷³, 89, F₄, 2, 131) (dual of [(89, 2), 5, 132]-NRT-code), using juxtaposition based on

linear OOA(4⁵, 5, F₄, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;5,4) [i]
linear OOA(4¹⁶³, 84, F₄, 2, 125) (dual of [(84, 2), 5, 126]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4³⁸, 21, F₄, 2, 31) (dual of [(21, 2), 4, 32]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,10P) [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, 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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