MinT - Information on Result #1021089

Information on Result #1021089

Linear OOA(3¹²⁷, 54, F₃, 3, 67) (dual of [(54, 3), 35, 68]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3³¹, 18, F₃, 3, 22) (dual of [(18, 3), 23, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3³¹, 19, F₃, 3, 22) (dual of [(19, 3), 26, 23]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,34P) [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3⁴², 18, F₃, 3, 33) (dual of [(18, 3), 12, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁴², 19, F₃, 3, 33) (dual of [(19, 3), 15, 34]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,23P) [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19 (see above)
linear OOA(3⁵⁴, 18, F₃, 3, 54) (dual of [(18, 3), 0, 55]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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