MinT - Information on Result #1159422

Information on Result #1159422

Linear OOA(2¹⁶⁴, large, F₂, 7, 9), using (u,Â u+v)-construction based on

linear OOA(2⁴⁴, 4194305, F₂, 7, 4) (dual of [(4194305, 7), 29360091, 5]-NRT-code), using
- appending 3 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(2¹²⁰, 4194304, F₂, 7, 9) (dual of [(4194304, 7), 29360008, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴, 3, F₂, 7, 4) (dual of [(3, 7), 17, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(7;17,2) [i]
  2. linear OOA(2¹¹⁶, 4194301, F₂, 7, 9) (dual of [(4194301, 7), 29359991, 10]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹¹⁶, large, F₂, 2, 9), 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(2¹⁶⁴, large, F₂, 7, 8)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁶⁴, large, F₂, 7, 7)	[i]
3	Linear OOA(2¹⁶⁴, large, F₂, 7, 6)	[i]
4	Linear OOA(2¹⁶⁴, large, F₂, 7, 5)	[i]
5	Linear OOA(2¹⁶⁴, large, F₂, 7, 4)	[i]
6	Linear OOA(2¹⁶⁴, large, F₂, 7, 3)	[i]
7	Linear OOA(2¹⁷¹, large, F₂, 7, 9)	[i]	NRT-Code Embedding in Larger Space
8	Linear OOA(2¹⁷⁸, large, F₂, 7, 9)	[i]
9	Linear OOA(2¹⁸⁵, large, F₂, 7, 9)	[i]
10	Linear OOA(2¹⁹², large, F₂, 7, 9)	[i]
11	Linear OOA(2¹⁹⁹, large, F₂, 7, 9)	[i]
12	Linear OOA(2²⁰⁶, large, F₂, 7, 9)	[i]
13	Linear OOA(2²¹³, large, F₂, 7, 9)	[i]
14	Linear OOA(2²²⁰, large, F₂, 7, 9)	[i]
15	Linear OOA(2²²⁷, large, F₂, 7, 9)	[i]
16	Linear OOA(2²³⁴, large, F₂, 7, 9)	[i]
17	Linear OOA(2²⁴¹, large, F₂, 7, 9)	[i]
18	Linear OOA(2²⁴⁸, large, F₂, 7, 9)	[i]
19	Linear OOA(2²⁵⁵, large, F₂, 7, 9)	[i]
20	Linear OOA(2¹⁶⁵, large, F₂, 7, 9)	[i]	OOA Duplication
21	Linear OOA(2¹⁶⁶, large, F₂, 7, 9)	[i]
22	Linear OOA(2¹⁶⁷, large, F₂, 7, 9)	[i]
23	Linear OOA(2¹⁶⁸, large, F₂, 7, 9)	[i]
24	Linear OOA(2¹⁶⁹, large, F₂, 7, 9)	[i]
25	Linear OOA(2¹⁷⁰, large, F₂, 7, 9)	[i]