MinT - Information on Result #548467

Information on Result #548467

There is no linear OA(3¹⁸², 188, F₃, 123) (dual of [188, 6, 124]-code), because residual code would yield linear OA(3⁵⁹, 64, F₃, 41) (dual of [64, 5, 42]-code), but

2 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(3¹⁸³, 189, F₃, 124) (dual of [189, 6, 125]-code)	[i]		Truncation
2	No linear OA(3¹⁸⁴, 190, F₃, 125) (dual of [190, 6, 126]-code)	[i]		Truncation
3	No linear OOA(3¹⁸², 188, F₃, 2, 123) (dual of [(188, 2), 194, 124]-NRT-code)	[i]		Depth Reduction
4	No linear OOA(3¹⁸², 188, F₃, 3, 123) (dual of [(188, 3), 382, 124]-NRT-code)	[i]
5	No linear OOA(3¹⁸², 188, F₃, 4, 123) (dual of [(188, 4), 570, 124]-NRT-code)	[i]
6	No linear OOA(3¹⁸², 188, F₃, 5, 123) (dual of [(188, 5), 758, 124]-NRT-code)	[i]