MinT - Information on Result #1143200

Information on Result #1143200

Linear OOA(2¹⁶³, large, F₂, 6, 8), using (u,Â u+v)-construction based on

linear OOA(2⁴⁴, 4194305, F₂, 6, 4) (dual of [(4194305, 6), 25165786, 5]-NRT-code), using
- appending 2 arbitrary columns [i] based on 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]
linear OOA(2¹¹⁹, 4194304, F₂, 6, 8) (dual of [(4194304, 6), 25165705, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴, 3, F₂, 6, 4) (dual of [(3, 6), 14, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(6;14,2) [i]
  2. linear OOA(2¹¹⁵, 4194301, F₂, 6, 8) (dual of [(4194301, 6), 25165691, 9]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹¹⁵, large, F₂, 2, 8), using
      - OOAs constructed from BCH codes [i]

Mode: Constructive and linear.

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

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁶³, large, F₂, 6, 7)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁶³, large, F₂, 6, 6)	[i]
3	Linear OOA(2¹⁶³, large, F₂, 6, 5)	[i]
4	Linear OOA(2¹⁶³, large, F₂, 6, 4)	[i]
5	Linear OOA(2¹⁶³, large, F₂, 6, 3)	[i]
6	Linear OOA(2¹⁶⁹, large, F₂, 6, 8)	[i]	NRT-Code Embedding in Larger Space
7	Linear OOA(2¹⁷⁵, large, F₂, 6, 8)	[i]
8	Linear OOA(2¹⁸¹, large, F₂, 6, 8)	[i]
9	Linear OOA(2¹⁸⁷, large, F₂, 6, 8)	[i]
10	Linear OOA(2¹⁹³, large, F₂, 6, 8)	[i]
11	Linear OOA(2¹⁹⁹, large, F₂, 6, 8)	[i]
12	Linear OOA(2²⁰⁵, large, F₂, 6, 8)	[i]
13	Linear OOA(2²¹¹, large, F₂, 6, 8)	[i]
14	Linear OOA(2²¹⁷, large, F₂, 6, 8)	[i]
15	Linear OOA(2²²³, large, F₂, 6, 8)	[i]
16	Linear OOA(2²²⁹, large, F₂, 6, 8)	[i]
17	Linear OOA(2²³⁵, large, F₂, 6, 8)	[i]
18	Linear OOA(2²⁴¹, large, F₂, 6, 8)	[i]
19	Linear OOA(2²⁴⁷, large, F₂, 6, 8)	[i]
20	Linear OOA(2²⁵³, large, F₂, 6, 8)	[i]
21	Linear OOA(2²⁵⁹, large, F₂, 6, 8)	[i]
22	Linear OOA(2¹⁶⁵, large, F₂, 6, 8)	[i]	OOA Duplication
23	Linear OOA(2¹⁶⁶, large, F₂, 6, 8)	[i]
24	Linear OOA(2¹⁶⁷, large, F₂, 6, 8)	[i]
25	Linear OOA(2¹⁶⁸, large, F₂, 6, 8)	[i]