MinT - Information on Result #1702844

Information on Result #1702844

Linear OOA(2²⁰⁸, 1878230, F₂, 8, 16) (dual of [(1878230, 8), 15025632, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁰⁸, 1878230, F₂, 4, 16) (dual of [(1878230, 4), 7512712, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁰⁸, 2097190, F₂, 4, 16) (dual of [(2097190, 4), 8388552, 17]-NRT-code), using
- strength reduction [i] based on linear OOA(2²⁰⁸, 2097190, F₂, 4, 17) (dual of [(2097190, 4), 8388552, 18]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2²¹, 39, F₂, 4, 8) (dual of [(39, 4), 135, 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(2¹⁸⁷, 2097151, F₂, 4, 17) (dual of [(2097151, 4), 8388417, 18]-NRT-code), using
      - OOA 2-folding [i] based on linear OOA(2¹⁸⁷, 4194302, F₂, 2, 17) (dual of [(4194302, 2), 8388417, 18]-NRT-code), using
        1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁸⁵, 4194301, F₂, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
        OOA 2-folding [i] based on linear OA(2¹⁸⁵, 8388602, F₂, 17) (dual of [8388602, 8388417, 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(2²⁰⁸, 1878229, F₂, 24, 16) (dual of [(1878229, 24), 45077288, 17]-NRT-code)	[i]		OOA Stacking with Additional Row