MinT - Information on Result #1653613

Information on Result #1653613

Linear OOA(2²⁵³, 1678403, F₂, 5, 19) (dual of [(1678403, 5), 8391762, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁵, 683, F₂, 5, 9) (dual of [(683, 5), 3370, 10]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁴⁵, 683, F₂, 3, 9) (dual of [(683, 3), 2004, 10]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁴⁵, 2049, F₂, 9) (dual of [2049, 2004, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
linear OOA(2²⁰⁸, 1677720, F₂, 5, 19) (dual of [(1677720, 5), 8388392, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2²⁰⁸, 8388600, F₂, 19) (dual of [8388600, 8388392, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁰⁸, large, F₂, 19) (dual of [large, large−208, 20]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁵³, 1678403, F₂, 6, 19) (dual of [(1678403, 6), 10070165, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵³, 1678403, F₂, 7, 19) (dual of [(1678403, 7), 11748568, 20]-NRT-code)	[i]
3	Linear OOA(2²⁵³, 1678403, F₂, 8, 19) (dual of [(1678403, 8), 13426971, 20]-NRT-code)	[i]
4	Digital (234, 253, 1678403)-net over F₂	[i]