MinT - Information on Result #2864660

Information on Result #2864660

Linear OOA(2²⁵¹, large, F₂, 5, 11), using 13 times NRT-code embedding in larger space based on linear OOA(2¹⁸⁶, 8388602, F₂, 5, 11) (dual of [(8388602, 5), 41942824, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. 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(2¹⁴⁰, 4194301, F₂, 5, 11) (dual of [(4194301, 5), 20971365, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹⁴⁰, 8388602, F₂, 3, 11) (dual of [(8388602, 3), 25165666, 12]-NRT-code), using
    - discarding factors / shortening the dual code 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		Method
1	Linear OOA(2²⁵², large, F₂, 5, 11)	[i]	OOA Duplication
2	Linear OOA(2²⁵³, large, F₂, 5, 11)	[i]
3	Linear OOA(2²⁵⁴, large, F₂, 5, 11)	[i]
4	Linear OOA(2²⁵⁵, large, F₂, 5, 11)	[i]