MinT - Information on Result #1616076

Information on Result #1616076

Linear OOA(2²²⁴, 2097649, F₂, 4, 16) (dual of [(2097649, 4), 8390372, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁰, 499, F₂, 4, 8) (dual of [(499, 4), 1956, 9]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁴⁰, 499, F₂, 2, 8) (dual of [(499, 2), 958, 9]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2⁴⁰, 512, F₂, 2, 8) (dual of [(512, 2), 984, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2⁴⁰, 1024, F₂, 8) (dual of [1024, 984, 9]-code), using
      - 1 times truncation [i] based on linear OA(2⁴¹, 1025, F₂, 9) (dual of [1025, 984, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 1025Â | 2²⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
linear OOA(2¹⁸⁴, 2097150, F₂, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹⁸⁴, 8388600, F₂, 16) (dual of [8388600, 8388416, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²²⁴, 2097649, F₂, 5, 16) (dual of [(2097649, 5), 10488021, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²⁴, 2097649, F₂, 6, 16) (dual of [(2097649, 6), 12585670, 17]-NRT-code)	[i]
3	Linear OOA(2²²⁴, 2097649, F₂, 7, 16) (dual of [(2097649, 7), 14683319, 17]-NRT-code)	[i]
4	Linear OOA(2²²⁴, 2097649, F₂, 8, 16) (dual of [(2097649, 8), 16780968, 17]-NRT-code)	[i]
5	Digital (208, 224, 2097649)-net over F₂	[i]