MinT - Information on Result #1631488

Information on Result #1631488

Linear OOA(2¹¹⁷, 2097151, F₂, 5, 10) (dual of [(2097151, 5), 10485638, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹⁷, 2097151, F₂, 4, 10) (dual of [(2097151, 4), 8388487, 11]-NRT-code), using

OOA 2-folding [i] based on linear OOA(2¹¹⁷, 4194302, F₂, 2, 10) (dual of [(4194302, 2), 8388487, 11]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹¹⁵, 4194301, F₂, 2, 10) (dual of [(4194301, 2), 8388487, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹¹⁵, 8388602, F₂, 10) (dual of [8388602, 8388487, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹¹⁵, large, F₂, 10) (dual of [large, large−115, 11]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹¹⁸, 2097151, F₂, 5, 10) (dual of [(2097151, 5), 10485637, 11]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹¹⁹, 2097151, F₂, 5, 10) (dual of [(2097151, 5), 10485636, 11]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹¹⁷, 2097150, F₂, 6, 10) (dual of [(2097150, 6), 12582783, 11]-NRT-code)	[i]	OOA Stacking with Additional Row
4	Linear OOA(2¹¹⁷, 2097150, F₂, 7, 10) (dual of [(2097150, 7), 14679933, 11]-NRT-code)	[i]
5	Linear OOA(2¹¹⁷, 2097150, F₂, 8, 10) (dual of [(2097150, 8), 16777083, 11]-NRT-code)	[i]
6	Linear OOA(2¹¹⁷, 2097150, F₂, 15, 10) (dual of [(2097150, 15), 31457133, 11]-NRT-code)	[i]