MinT - Information on Result #2788050

Information on Result #2788050

Linear OOA(2¹⁶⁴, large, F₂, 4, 9), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁶⁰, 8388602, F₂, 4, 9) (dual of [(8388602, 4), 33554248, 10]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁴⁴, 4194305, F₂, 4, 4) (dual of [(4194305, 4), 16777176, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(2⁴⁴, 4194305, F₂, 3, 4) (dual of [(4194305, 3), 12582871, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (40, 44, 4194305)-net over F₂, using
      - nets constructed from net-embeddable BCH codes [i]
2. linear OOA(2¹¹⁶, 4194301, F₂, 4, 9) (dual of [(4194301, 4), 16777088, 10]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹¹⁶, 8388602, F₂, 2, 9) (dual of [(8388602, 2), 16777088, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2¹¹⁶, large, F₂, 2, 9), using
      - OOAs constructed from BCH codes [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁶⁵, large, F₂, 4, 9)	[i]	OOA Duplication
2	Linear OOA(2¹⁶⁶, large, F₂, 4, 9)	[i]
3	Linear OOA(2¹⁶⁷, large, F₂, 4, 9)	[i]
4	Linear OOA(2¹⁶⁴, 8388602, F₂, 5, 9) (dual of [(8388602, 5), 41942846, 10]-NRT-code)	[i]	OOA Stacking with Additional Row
5	Linear OOA(2¹⁶⁴, 8388602, F₂, 6, 9) (dual of [(8388602, 6), 50331448, 10]-NRT-code)	[i]
6	Linear OOA(2¹⁶⁴, 8388602, F₂, 7, 9) (dual of [(8388602, 7), 58720050, 10]-NRT-code)	[i]
7	Linear OOA(2¹⁶⁴, 8388602, F₂, 8, 9) (dual of [(8388602, 8), 67108652, 10]-NRT-code)	[i]