MinT - Information on Result #2227250

Information on Result #2227250

Linear OA(3⁴⁸, 54, F₃, 33) (dual of [54, 6, 34]-code), using 2 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, 33) (dual of [57, 6, 34]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(3⁵², 58, F₃, 33) (dual of [58, 6, 34]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(3¹²⁹, 134, F₃, 87) (dual of [134, 5, 88]-code)	[i]		Juxtaposition
4	Linear OOA(3⁴⁸, 27, F₃, 2, 33) (dual of [(27, 2), 6, 34]-NRT-code)	[i]		OOA Folding
5	Linear OOA(3⁴⁸, 18, F₃, 3, 33) (dual of [(18, 3), 6, 34]-NRT-code)	[i]		OOA Folding