MinT - Information on Result #671904

Information on Result #671904

Linear OA(3¹⁸⁰, 187, F₃, 116) (dual of [187, 7, 117]-code), using juxtaposition based on

linear OA(3¹², 19, F₃, 8) (dual of [19, 7, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹², 24, F₃, 8) (dual of [24, 12, 9]-code), using
  - extended quadratic residue code Q_e(24,3) [i]
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
      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]
  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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3¹⁸⁰, 187, F₃, 115) (dual of [187, 7, 116]-code)	[i]		Strength Reduction