MinT - Information on Result #1021241

Information on Result #1021241

Linear OOA(4²¹⁰, 76, F₄, 3, 143) (dual of [(76, 3), 18, 144]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(4⁴², 19, F₄, 3, 35) (dual of [(19, 3), 15, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁴², 21, F₄, 3, 35) (dual of [(21, 3), 21, 36]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,27P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4⁵⁴, 19, F₄, 3, 47) (dual of [(19, 3), 3, 48]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁵⁴, 21, F₄, 3, 47) (dual of [(21, 3), 9, 48]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,15P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21 (see above)
linear OOA(4⁵⁷, 19, F₄, 3, 57) (dual of [(19, 3), 0, 58]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]
linear OOA(4⁵⁷, 19, F₄, 3, 57) (dual of [(19, 3), 0, 58]-NRT-code) (see above)

Mode: Constructive and linear.

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