MinT - Information on Result #641025

Information on Result #641025

Linear OA(3¹²⁹, 134, F₃, 87) (dual of [134, 5, 88]-code), using juxtaposition based on

linear OA(3⁴⁸, 53, F₃, 33) (dual of [53, 5, 34]-code), using
- discarding factors / shortening the dual code 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]
linear OA(3⁷⁶, 81, F₃, 53) (dual of [81, 5, 54]-code), using
- a code of Belov type defined by PG(4,3) ∖ PG(3,3) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹²⁹, 67, F₃, 2, 87) (dual of [(67, 2), 5, 88]-NRT-code)	[i]		OOA Folding