MinT - Information on Result #641006

Information on Result #641006

Linear OA(3⁵⁹, 64, F₃, 39) (dual of [64, 5, 40]-code), using juxtaposition based on

linear OA(3⁴, 9, F₃, 3) (dual of [9, 5, 4]-code or 9-cap in PG(3,3)), using
- discarding factors / shortening the dual code based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
  - ovoid in PG(3,Â 3) [i]
linear OA(3⁵⁰, 55, F₃, 35) (dual of [55, 5, 36]-code), using
- discarding factors / shortening the dual code 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:

	Result		This result only	Method
1	Linear OOA(3⁵⁹, 32, F₃, 2, 39) (dual of [(32, 2), 5, 40]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3⁵⁹, 21, F₃, 3, 39) (dual of [(21, 3), 4, 40]-NRT-code)	[i]		OOA Folding