MinT - Information on Result #2959672

Information on Result #2959672

Linear OOA(2²³⁹, large, F₂, 7, 10), using 7 times NRT-code embedding in larger space based on linear OOA(2¹⁹⁰, large, F₂, 7, 10), 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(2¹⁴⁴, 4194303, F₂, 7, 10) (dual of [(4194303, 7), 29359977, 11]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2¹⁴⁴, 4194304, F₂, 5, 10) (dual of [(4194304, 5), 20971376, 11]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁵, 3, F₂, 5, 5) (dual of [(3, 5), 10, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(5;10,2) [i]
      2. linear OOA(2¹³⁹, 4194301, F₂, 5, 10) (dual of [(4194301, 5), 20971366, 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.

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(2²⁴⁰, large, F₂, 7, 10)	[i]		OOA Duplication
2	Linear OOA(2²⁴¹, large, F₂, 7, 10)	[i]
3	Linear OOA(2²⁴², large, F₂, 7, 10)	[i]
4	Linear OOA(2²⁴³, large, F₂, 7, 10)	[i]
5	Linear OOA(2²⁴⁴, large, F₂, 7, 10)	[i]
6	Linear OOA(2²⁴⁵, large, F₂, 7, 10)	[i]