MinT - Information on Result #2920609

Information on Result #2920609

Linear OOA(2²⁴², large, F₂, 6, 9), using 13 times NRT-code embedding in larger space based on linear OOA(2¹⁶⁴, large, F₂, 6, 9), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁴⁴, 4194305, F₂, 6, 4) (dual of [(4194305, 6), 25165786, 5]-NRT-code), using
  - appending 2 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]
2. linear OOA(2¹²⁰, 4194304, F₂, 6, 9) (dual of [(4194304, 6), 25165704, 10]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁴, 3, F₂, 6, 4) (dual of [(3, 6), 14, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(6;14,2) [i]
    2. linear OOA(2¹¹⁶, 4194301, F₂, 6, 9) (dual of [(4194301, 6), 25165690, 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.

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(2²⁴³, large, F₂, 6, 9)	[i]		OOA Duplication
2	Linear OOA(2²⁴⁴, large, F₂, 6, 9)	[i]
3	Linear OOA(2²⁴⁵, large, F₂, 6, 9)	[i]
4	Linear OOA(2²⁴⁶, large, F₂, 6, 9)	[i]
5	Linear OOA(2²⁴⁷, large, F₂, 6, 9)	[i]