MinT - Information on Result #1599811

Information on Result #1599811

Linear OOA(2²⁴⁹, 2817196, F₂, 4, 17) (dual of [(2817196, 4), 11268535, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁹, 2817196, F₂, 3, 17) (dual of [(2817196, 3), 8451339, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴⁹, 2818046, F₂, 3, 17) (dual of [(2818046, 3), 8453889, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁶⁴, 21845, F₂, 3, 8) (dual of [(21845, 3), 65471, 9]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2⁶⁴, 65535, F₂, 8) (dual of [65535, 65471, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(2⁶⁴, 65536, F₂, 8) (dual of [65536, 65472, 9]-code), using
        1 times truncation [i] based on linear OA(2⁶⁵, 65537, F₂, 9) (dual of [65537, 65472, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
  2. linear OOA(2¹⁸⁵, 2796201, F₂, 3, 17) (dual of [(2796201, 3), 8388418, 18]-NRT-code), using
    - OOA 3-folding [i] 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(2²⁴⁹, 1408598, F₂, 7, 17) (dual of [(1408598, 7), 9859937, 18]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁴⁹, 1408598, F₂, 8, 17) (dual of [(1408598, 8), 11268535, 18]-NRT-code)	[i]		OOA Folding