MinT - Information on Result #548465

Information on Result #548465

There is no linear OA(3¹⁷⁸, 184, F₃, 120) (dual of [184, 6, 121]-code), because residual code would yield linear OA(3⁵⁸, 63, F₃, 40) (dual of [63, 5, 41]-code), but

1 times truncation [i] would yield linear OA(3⁵⁷, 62, F₃, 39) (dual of [62, 5, 40]-code), but
- residual code [i] would yield linear OA(3¹⁸, 22, F₃, 13) (dual of [22, 4, 14]-code), but
  - 1 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
    - â€œHNâ€ bound on codes from Brouwerâ€™s database [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(3¹⁷⁹, 185, F₃, 121) (dual of [185, 6, 122]-code)	[i]		Truncation
2	No linear OA(3¹⁸⁰, 186, F₃, 122) (dual of [186, 6, 123]-code)	[i]		Truncation
3	No linear OOA(3¹⁷⁸, 184, F₃, 2, 120) (dual of [(184, 2), 190, 121]-NRT-code)	[i]		Depth Reduction
4	No linear OOA(3¹⁷⁸, 184, F₃, 3, 120) (dual of [(184, 3), 374, 121]-NRT-code)	[i]
5	No linear OOA(3¹⁷⁸, 184, F₃, 4, 120) (dual of [(184, 4), 558, 121]-NRT-code)	[i]
6	No linear OOA(3¹⁷⁸, 184, F₃, 5, 120) (dual of [(184, 5), 742, 121]-NRT-code)	[i]
7	No linear OA(3¹⁷⁹, 188, F₃, 120) (dual of [188, 9, 121]-code)	[i]		ConstructionÂ Y1 (Bound)