MinT - Information on Result #1143315

Information on Result #1143315

Linear OOA(2¹⁹⁰, large, F₂, 6, 10), using (u,Â u+v)-construction based on

linear OOA(2⁴⁶, 4194305, F₂, 6, 5) (dual of [(4194305, 6), 25165784, 6]-NRT-code), using
- appending 1 arbitrary column [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(2¹⁴⁴, 4194304, F₂, 6, 10) (dual of [(4194304, 6), 25165680, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁵, 3, F₂, 6, 5) (dual of [(3, 6), 13, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(6;13,2) [i]
  2. linear OOA(2¹³⁹, 4194301, F₂, 6, 10) (dual of [(4194301, 6), 25165667, 11]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(2¹³⁹, 8388602, F₂, 3, 10) (dual of [(8388602, 3), 25165667, 11]-NRT-code), using
      - 1 step truncation [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(2¹⁹⁰, large, F₂, 6, 9)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁹⁰, large, F₂, 6, 8)	[i]
3	Linear OOA(2¹⁹⁰, large, F₂, 6, 7)	[i]
4	Linear OOA(2¹⁹⁰, large, F₂, 6, 6)	[i]
5	Linear OOA(2¹⁹⁰, large, F₂, 6, 5)	[i]
6	Linear OOA(2¹⁹⁰, large, F₂, 6, 4)	[i]
7	Linear OOA(2¹⁹⁰, large, F₂, 6, 3)	[i]
8	Linear OOA(2¹⁹⁶, large, F₂, 6, 10)	[i]	NRT-Code Embedding in Larger Space
9	Linear OOA(2²⁰², large, F₂, 6, 10)	[i]
10	Linear OOA(2²⁰⁸, large, F₂, 6, 10)	[i]
11	Linear OOA(2²¹⁴, large, F₂, 6, 10)	[i]
12	Linear OOA(2²²⁰, large, F₂, 6, 10)	[i]
13	Linear OOA(2²²⁶, large, F₂, 6, 10)	[i]
14	Linear OOA(2²³², large, F₂, 6, 10)	[i]
15	Linear OOA(2²³⁸, large, F₂, 6, 10)	[i]
16	Linear OOA(2²⁴⁴, large, F₂, 6, 10)	[i]
17	Linear OOA(2²⁵⁰, large, F₂, 6, 10)	[i]
18	Linear OOA(2²⁵⁶, large, F₂, 6, 10)	[i]
19	Linear OOA(2¹⁹², large, F₂, 6, 10)	[i]	OOA Duplication
20	Linear OOA(2¹⁹³, large, F₂, 6, 10)	[i]
21	Linear OOA(2¹⁹⁴, large, F₂, 6, 10)	[i]
22	Linear OOA(2¹⁹⁵, large, F₂, 6, 10)	[i]