MinT - Information on Result #1702696

Information on Result #1702696

Linear OOA(2²⁰⁶, 1554708, F₂, 8, 17) (dual of [(1554708, 8), 12437458, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁰⁶, 1554708, F₂, 5, 17) (dual of [(1554708, 5), 7773334, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁰⁶, 1677759, F₂, 5, 17) (dual of [(1677759, 5), 8388589, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²¹, 39, F₂, 5, 8) (dual of [(39, 5), 174, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (13, 21, 39)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁸⁵, 1677720, F₂, 5, 17) (dual of [(1677720, 5), 8388415, 18]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2¹⁸⁵, 8388600, F₂, 17) (dual of [8388600, 8388415, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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(2²⁰⁶, 1554707, F₂, 24, 17) (dual of [(1554707, 24), 37312762, 18]-NRT-code)	[i]		OOA Stacking with Additional Row