MinT - Information on Result #547795

Information on Result #547795

There is no linear OA(3¹⁵¹, 158, F₃, 102) (dual of [158, 7, 103]-code), because constructionÂ Y1 would yield

linear OA(3¹⁵⁰, 155, F₃, 102) (dual of [155, 5, 103]-code), but
- Griesmer bound [i]
linear OA(3⁷, 158, F₃, 3) (dual of [158, 151, 4]-code or 158-cap in PG(6,3)), but
- discarding factors / shortening the dual code would yield linear OA(3⁷, 137, F₃, 3) (dual of [137, 130, 4]-code or 137-cap in PG(6,3)), but
  - a result by BarÃ¡t, Edel, Hill, and Storme [i]

Mode: Bound (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	No linear OA(3¹⁵², 159, F₃, 103) (dual of [159, 7, 104]-code)	[i]		Truncation
2	No linear OA(3¹⁵³, 160, F₃, 104) (dual of [160, 7, 105]-code)	[i]		Truncation
3	No linear OOA(3¹⁵¹, 158, F₃, 2, 102) (dual of [(158, 2), 165, 103]-NRT-code)	[i]		Depth Reduction
4	No linear OOA(3¹⁵¹, 158, F₃, 3, 102) (dual of [(158, 3), 323, 103]-NRT-code)	[i]
5	No linear OOA(3¹⁵¹, 158, F₃, 4, 102) (dual of [(158, 4), 481, 103]-NRT-code)	[i]
6	No linear OOA(3¹⁵¹, 158, F₃, 5, 102) (dual of [(158, 5), 639, 103]-NRT-code)	[i]