MinT - Information on Result #2227249

Information on Result #2227249

Linear OA(3⁴⁹, 55, F₃, 34) (dual of [55, 6, 35]-code), using 1 times truncation 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.

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(3⁵¹, 57, F₃, 34) (dual of [57, 6, 35]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(3⁵², 58, F₃, 34) (dual of [58, 6, 35]-code)	[i]
3	Linear OA(3⁵³, 59, F₃, 34) (dual of [59, 6, 35]-code)	[i]
4	Linear OA(3¹³⁰, 135, F₃, 88) (dual of [135, 5, 89]-code)	[i]		Juxtaposition
5	Linear OOA(3⁴⁹, 27, F₃, 2, 34) (dual of [(27, 2), 5, 35]-NRT-code)	[i]		OOA Folding
6	Linear OOA(3⁴⁹, 18, F₃, 3, 34) (dual of [(18, 3), 5, 35]-NRT-code)	[i]		OOA Folding