MinT - Information on Result #1021250

Information on Result #1021250

Linear OOA(4²⁰⁶, 76, F₄, 3, 135) (dual of [(76, 3), 22, 136]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(4⁴⁰, 19, F₄, 3, 33) (dual of [(19, 3), 17, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁴⁰, 21, F₄, 3, 33) (dual of [(21, 3), 23, 34]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,29P) [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(4⁵², 19, F₄, 3, 45) (dual of [(19, 3), 5, 46]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁵², 21, F₄, 3, 45) (dual of [(21, 3), 11, 46]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,17P) [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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