MinT - Information on Result #548435

Information on Result #548435

There is no linear OA(2²⁵⁹, 269, F₂, 130) (dual of [269, 10, 131]-code), because residual code would yield linear OA(2¹²⁹, 138, F₂, 65) (dual of [138, 9, 66]-code), but

1 times truncation [i] would yield linear OA(2¹²⁸, 137, F₂, 64) (dual of [137, 9, 65]-code), but
- residual code [i] would yield linear OA(2⁶⁴, 72, F₂, 32) (dual of [72, 8, 33]-code), but
  - adding a parity check bit [i] would yield linear OA(2⁶⁵, 73, F₂, 33) (dual of [73, 8, 34]-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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No linear OA(2²⁶⁰, 270, F₂, 131) (dual of [270, 10, 132]-code)	[i]		Truncation
2	No linear OOA(2²⁶⁰, 269, F₂, 2, 131) (dual of [(269, 2), 278, 132]-NRT-code)	[i]		m-Reduction for OOAs
3	No linear OOA(2²⁵⁹, 269, F₂, 2, 130) (dual of [(269, 2), 279, 131]-NRT-code)	[i]		Depth Reduction
4	No linear OOA(2²⁵⁹, 269, F₂, 3, 130) (dual of [(269, 3), 548, 131]-NRT-code)	[i]
5	No linear OOA(2²⁵⁹, 269, F₂, 4, 130) (dual of [(269, 4), 817, 131]-NRT-code)	[i]
6	No linear OOA(2²⁵⁹, 269, F₂, 5, 130) (dual of [(269, 5), 1086, 131]-NRT-code)	[i]
7	No linear OOA(2²⁵⁹, 269, F₂, 6, 130) (dual of [(269, 6), 1355, 131]-NRT-code)	[i]
8	No linear OOA(2²⁵⁹, 269, F₂, 7, 130) (dual of [(269, 7), 1624, 131]-NRT-code)	[i]
9	No linear OOA(2²⁵⁹, 269, F₂, 8, 130) (dual of [(269, 8), 1893, 131]-NRT-code)	[i]
10	No digital (129, 259, 269)-net over F₂	[i]		Extracting Embedded Orthogonal Array
11	No linear OA(2²⁶⁰, 273, F₂, 130) (dual of [273, 13, 131]-code)	[i]		ConstructionÂ Y1 (Bound)