MinT - Information on Result #640992

Information on Result #640992

Linear OA(3⁶¹, 67, F₃, 40) (dual of [67, 6, 41]-code), using juxtaposition based on

linear OA(3⁵, 11, F₃, 4) (dual of [11, 6, 5]-code), using
- Golay code G(3) [i]
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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3⁶¹, 67, F₃, 39) (dual of [67, 6, 40]-code)	[i]		Strength Reduction
2	Linear OA(3⁶¹, 67, F₃, 38) (dual of [67, 6, 39]-code)	[i]		Strength Reduction
3	Linear OOA(3⁶¹, 33, F₃, 2, 40) (dual of [(33, 2), 5, 41]-NRT-code)	[i]		OOA Folding
4	Linear OOA(3⁶¹, 22, F₃, 3, 40) (dual of [(22, 3), 5, 41]-NRT-code)	[i]		OOA Folding