MinT - Information on Result #2959770

Information on Result #2959770

Linear OOA(2²¹², large, F₂, 7, 11), using 3 times NRT-code embedding in larger space based on linear OOA(2¹⁹¹, large, F₂, 7, 11), using

(u,Â u+v)-construction [i] based on
1. 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]
2. 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.

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		This result only	Method
1	Linear OOA(2²¹³, large, F₂, 7, 11)	[i]		OOA Duplication
2	Linear OOA(2²¹⁴, large, F₂, 7, 11)	[i]
3	Linear OOA(2²¹⁵, large, F₂, 7, 11)	[i]
4	Linear OOA(2²¹⁶, large, F₂, 7, 11)	[i]
5	Linear OOA(2²¹⁷, large, F₂, 7, 11)	[i]
6	Linear OOA(2²¹⁸, large, F₂, 7, 11)	[i]