MinT - Information on Result #906117

Information on Result #906117

Linear OOA(3¹³⁹, 81, F₃, 2, 67) (dual of [(81, 2), 23, 68]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3³⁷, 27, F₃, 2, 22) (dual of [(27, 2), 17, 23]-NRT-code), using
- algebraic-geometric NRT-code AG(2;F,31P) [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(3⁴⁸, 27, F₃, 2, 33) (dual of [(27, 2), 6, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁴⁸, 54, F₃, 33) (dual of [54, 6, 34]-code), using
  - 2 times truncation [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]
- algebraic-geometric NRT-code AG(2;F,20P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
linear OOA(3⁵⁴, 27, F₃, 2, 54) (dual of [(27, 2), 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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