MinT - Information on Result #1653581

Information on Result #1653581

Linear OOA(2²¹⁷, 1677848, F₂, 5, 17) (dual of [(1677848, 5), 8389023, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³², 128, F₂, 5, 8) (dual of [(128, 5), 608, 9]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2³², 128, F₂, 2, 8) (dual of [(128, 2), 224, 9]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2³², 256, F₂, 8) (dual of [256, 224, 9]-code), using
    - 1 times truncation [i] based on linear OA(2³³, 257, F₂, 9) (dual of [257, 224, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 257Â | 2¹⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
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.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²¹⁷, 1677848, F₂, 6, 17) (dual of [(1677848, 6), 10066871, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹⁷, 1677848, F₂, 7, 17) (dual of [(1677848, 7), 11744719, 18]-NRT-code)	[i]
3	Linear OOA(2²¹⁷, 1677848, F₂, 8, 17) (dual of [(1677848, 8), 13422567, 18]-NRT-code)	[i]
4	Digital (200, 217, 1677848)-net over F₂	[i]