MinT - Information on Result #547796

Information on Result #547796

There is no linear OA(3¹⁵⁵, 162, F₃, 105) (dual of [162, 7, 106]-code), because constructionÂ Y1 would yield

linear OA(3¹⁵⁴, 159, F₃, 105) (dual of [159, 5, 106]-code), but
- Griesmer bound [i]
linear OA(3⁷, 162, F₃, 3) (dual of [162, 155, 4]-code or 162-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(3¹⁵⁶, 163, F₃, 106) (dual of [163, 7, 107]-code)	[i]		Truncation
2	No linear OA(3¹⁵⁷, 164, F₃, 107) (dual of [164, 7, 108]-code)	[i]		Truncation
3	No linear OOA(3¹⁵⁵, 162, F₃, 2, 105) (dual of [(162, 2), 169, 106]-NRT-code)	[i]		Depth Reduction
4	No linear OOA(3¹⁵⁵, 162, F₃, 3, 105) (dual of [(162, 3), 331, 106]-NRT-code)	[i]
5	No linear OOA(3¹⁵⁵, 162, F₃, 4, 105) (dual of [(162, 4), 493, 106]-NRT-code)	[i]
6	No linear OOA(3¹⁵⁵, 162, F₃, 5, 105) (dual of [(162, 5), 655, 106]-NRT-code)	[i]