MinT - Information on Result #909081

Information on Result #909081

Linear OOA(3¹⁷⁵, 91, F₃, 2, 114) (dual of [(91, 2), 7, 115]-NRT-code), using juxtaposition 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(3¹⁶¹, 84, F₃, 2, 107) (dual of [(84, 2), 7, 108]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁶¹, 168, F₃, 107) (dual of [168, 7, 108]-code), using
  - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
    1. 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
        linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
        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]
    2. linear OA(3⁵⁵, 56, F₃, 53) (dual of [56, 1, 54]-code), using
      - strength reduction [i] based on linear OA(3⁵⁵, 56, F₃, 55) (dual of [56, 1, 56]-code or 56-arc in PG(54,3)), using
        dual of repetition code with length 56 [i]
    3. linear OA(3⁵⁶, 56, F₃, 56) (dual of [56, 0, 57]-code or 56-arc in PG(55,3)), using
      - complete OA / dual of code with only one code word [i]

Mode: Constructive and linear.

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