MinT - Information on Result #1513967

Information on Result #1513967

Linear OOA(2¹⁸⁰, 3727815, F₂, 3, 12) (dual of [(3727815, 3), 11183265, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁸⁰, 3727815, F₂, 2, 12) (dual of [(3727815, 2), 7455450, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁸⁰, 4202493, F₂, 2, 12) (dual of [(4202493, 2), 8404806, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁷⁸, 4202492, F₂, 2, 12) (dual of [(4202492, 2), 8404806, 13]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁴⁰, 8191, F₂, 2, 6) (dual of [(8191, 2), 16342, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F₂, using
        1 times m-reduction [i] based on digital (34, 41, 8191)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
    2. linear OOA(2¹³⁸, 4194301, F₂, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2¹³⁸, 8388602, F₂, 12) (dual of [8388602, 8388464, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, 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(2¹⁸⁰, 1863907, F₂, 5, 12) (dual of [(1863907, 5), 9319355, 13]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁸⁰, 1863907, F₂, 6, 12) (dual of [(1863907, 6), 11183262, 13]-NRT-code)	[i]		OOA Folding