MinT - Information on Result #1159516

Information on Result #1159516

Linear OOA(2¹⁹¹, large, F₂, 7, 11), using (u,Â u+v)-construction based on

linear OOA(2⁴⁶, 4194305, F₂, 7, 5) (dual of [(4194305, 7), 29360089, 6]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(2⁴⁶, 4194305, F₂, 5, 5) (dual of [(4194305, 5), 20971479, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(2⁴⁶, 4194305, F₂, 4, 5) (dual of [(4194305, 4), 16777174, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (41, 46, 4194305)-net over F₂, using
      - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁴⁵, 4194304, F₂, 7, 11) (dual of [(4194304, 7), 29359983, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁵, 3, F₂, 7, 5) (dual of [(3, 7), 16, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(7;16,2) [i]
  2. linear OOA(2¹⁴⁰, 4194301, F₂, 7, 11) (dual of [(4194301, 7), 29359967, 12]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), 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(2¹⁹¹, large, F₂, 7, 10)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁹¹, large, F₂, 7, 9)	[i]
3	Linear OOA(2¹⁹¹, large, F₂, 7, 8)	[i]
4	Linear OOA(2¹⁹¹, large, F₂, 7, 7)	[i]
5	Linear OOA(2¹⁹¹, large, F₂, 7, 6)	[i]
6	Linear OOA(2¹⁹¹, large, F₂, 7, 5)	[i]
7	Linear OOA(2¹⁹¹, large, F₂, 7, 4)	[i]
8	Linear OOA(2¹⁹¹, large, F₂, 7, 3)	[i]
9	Linear OOA(2¹⁹⁸, large, F₂, 7, 11)	[i]	NRT-Code Embedding in Larger Space
10	Linear OOA(2²⁰⁵, large, F₂, 7, 11)	[i]
11	Linear OOA(2²¹², large, F₂, 7, 11)	[i]
12	Linear OOA(2²¹⁹, large, F₂, 7, 11)	[i]
13	Linear OOA(2²²⁶, large, F₂, 7, 11)	[i]
14	Linear OOA(2²³³, large, F₂, 7, 11)	[i]
15	Linear OOA(2²⁴⁰, large, F₂, 7, 11)	[i]
16	Linear OOA(2²⁴⁷, large, F₂, 7, 11)	[i]
17	Linear OOA(2²⁵⁴, large, F₂, 7, 11)	[i]
18	Linear OOA(2¹⁹², large, F₂, 7, 11)	[i]	OOA Duplication
19	Linear OOA(2¹⁹³, large, F₂, 7, 11)	[i]
20	Linear OOA(2¹⁹⁴, large, F₂, 7, 11)	[i]
21	Linear OOA(2¹⁹⁵, large, F₂, 7, 11)	[i]
22	Linear OOA(2¹⁹⁶, large, F₂, 7, 11)	[i]
23	Linear OOA(2¹⁹⁷, large, F₂, 7, 11)	[i]