MinT - Information on Result #909158

Information on Result #909158

Linear OOA(3¹⁵⁹, 82, F₃, 2, 108) (dual of [(82, 2), 5, 109]-NRT-code), using juxtaposition based on

linear OOA(3⁷, 6, F₃, 2, 6) (dual of [(6, 2), 5, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁷, 7, F₃, 2, 6) (dual of [(7, 2), 7, 7]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁴⁷, 76, F₃, 2, 101) (dual of [(76, 2), 5, 102]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(3⁷¹, 38, F₃, 2, 50) (dual of [(38, 2), 5, 51]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(3²⁰, 12, F₃, 2, 16) (dual of [(12, 2), 4, 17]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(3²⁵, 13, F₃, 2, 25) (dual of [(13, 2), 1, 26]-NRT-code), using
      - dual of repetition NRT-code with length 13 [i]
    3. linear OOA(3²⁶, 13, F₃, 2, 26) (dual of [(13, 2), 0, 27]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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