MinT - Information on Result #1673322

Information on Result #1673322

Linear OOA(2²⁵⁸, 1398131, F₂, 6, 21) (dual of [(1398131, 6), 8388528, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁷, 31, F₂, 6, 10) (dual of [(31, 6), 159, 11]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁷, 31, F₂, 2, 10) (dual of [(31, 2), 35, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2²⁷, 62, F₂, 10) (dual of [62, 35, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²⁷, 63, F₂, 10) (dual of [63, 36, 11]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
linear OOA(2²³¹, 1398100, F₂, 6, 21) (dual of [(1398100, 6), 8388369, 22]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2²³¹, 8388600, F₂, 21) (dual of [8388600, 8388369, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²³¹, large, F₂, 21) (dual of [large, large−231, 22]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁵⁸, 1398131, F₂, 7, 21) (dual of [(1398131, 7), 9786659, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵⁸, 1398131, F₂, 8, 21) (dual of [(1398131, 8), 11184790, 22]-NRT-code)	[i]
3	Digital (237, 258, 1398131)-net over F₂	[i]