MinT - Information on Result #1664350

Information on Result #1664350

Linear OOA(2¹⁴⁰, 2097151, F₂, 6, 12) (dual of [(2097151, 6), 12582766, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁴⁰, 2097151, F₂, 4, 12) (dual of [(2097151, 4), 8388464, 13]-NRT-code), using

OOA 2-folding [i] based on linear OOA(2¹⁴⁰, 4194302, F₂, 2, 12) (dual of [(4194302, 2), 8388464, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹³⁸, 4194301, F₂, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹³⁸, 8388602, F₂, 12) (dual of [8388602, 8388464, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁴¹, 2097151, F₂, 6, 12) (dual of [(2097151, 6), 12582765, 13]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁴², 2097151, F₂, 6, 12) (dual of [(2097151, 6), 12582764, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁴³, 2097151, F₂, 6, 12) (dual of [(2097151, 6), 12582763, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁴⁰, 2097150, F₂, 7, 12) (dual of [(2097150, 7), 14679910, 13]-NRT-code)	[i]	OOA Stacking with Additional Row
5	Linear OOA(2¹⁴⁰, 2097150, F₂, 8, 12) (dual of [(2097150, 8), 16777060, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁴⁰, 2097150, F₂, 18, 12) (dual of [(2097150, 18), 37748560, 13]-NRT-code)	[i]