MinT - Information on Result #548420

Information on Result #548420

There is no linear OA(2²³⁷, 247, F₂, 120) (dual of [247, 10, 121]-code), because residual code would yield linear OA(2¹¹⁷, 126, F₂, 60) (dual of [126, 9, 61]-code), but

residual code [i] would yield linear OA(2⁵⁷, 65, F₂, 30) (dual of [65, 8, 31]-code), but
- 2 times truncation [i] would yield linear OA(2⁵⁵, 63, F₂, 28) (dual of [63, 8, 29]-code), but
  - â€œBJVâ€ 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(2²³⁸, 248, F₂, 121) (dual of [248, 10, 122]-code)	[i]		Truncation
2	No linear OA(2²⁴⁰, 250, F₂, 123) (dual of [250, 10, 124]-code)	[i]		Truncation
3	No linear OOA(2²³⁸, 247, F₂, 2, 121) (dual of [(247, 2), 256, 122]-NRT-code)	[i]		m-Reduction for OOAs
4	No linear OOA(2²³⁹, 247, F₂, 2, 122) (dual of [(247, 2), 255, 123]-NRT-code)	[i]
5	No linear OOA(2²⁴⁰, 247, F₂, 2, 123) (dual of [(247, 2), 254, 124]-NRT-code)	[i]
6	No linear OOA(2²³⁷, 247, F₂, 2, 120) (dual of [(247, 2), 257, 121]-NRT-code)	[i]		Depth Reduction
7	No linear OOA(2²³⁷, 247, F₂, 3, 120) (dual of [(247, 3), 504, 121]-NRT-code)	[i]
8	No linear OOA(2²³⁷, 247, F₂, 4, 120) (dual of [(247, 4), 751, 121]-NRT-code)	[i]
9	No linear OOA(2²³⁷, 247, F₂, 5, 120) (dual of [(247, 5), 998, 121]-NRT-code)	[i]
10	No linear OOA(2²³⁷, 247, F₂, 6, 120) (dual of [(247, 6), 1245, 121]-NRT-code)	[i]
11	No linear OOA(2²³⁷, 247, F₂, 7, 120) (dual of [(247, 7), 1492, 121]-NRT-code)	[i]
12	No linear OOA(2²³⁷, 247, F₂, 8, 120) (dual of [(247, 8), 1739, 121]-NRT-code)	[i]
13	No digital (117, 237, 247)-net over F₂	[i]		Extracting Embedded Orthogonal Array