MinT - Information on Result #906111

Information on Result #906111

Linear OOA(3¹⁴⁴, 84, F₃, 2, 71) (dual of [(84, 2), 24, 72]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3³⁸, 28, F₃, 2, 23) (dual of [(28, 2), 18, 24]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,32P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3⁵⁰, 28, F₃, 2, 35) (dual of [(28, 2), 6, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
  - dual code (with bound on d by constructionÂ Y1) [i] based on
    1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
      - the Hill cap [i]
    2. nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
      - 20 is the largest size of a cap in PG(4,Â 3) [i]
linear OOA(3⁵⁶, 28, F₃, 2, 56) (dual of [(28, 2), 0, 57]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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