MinT - Information on Result #661895

Information on Result #661895

Linear OA(3⁸³, 118, F₃, 35) (dual of [118, 35, 36]-code), using (u,Â u+v)-construction based on

linear OA(3³⁰, 59, F₃, 17) (dual of [59, 29, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3³⁰, 60, F₃, 17) (dual of [60, 30, 18]-code), using
  - extended quadratic residue code Q_e(60,3) [i]
linear OA(3⁵³, 59, F₃, 35) (dual of [59, 6, 36]-code), using
- 3 times code embedding in larger space [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]

Mode: Constructive and linear.

None.

The following results depend on this result: