MinT - Information on Result #1079595

Information on Result #1079595

Linear OOA(2¹⁴⁴, 2097153, F₂, 4, 12) (dual of [(2097153, 4), 8388468, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶, 3, F₂, 4, 6) (dual of [(3, 4), 6, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(4;6,2) [i]
linear OOA(2¹³⁸, 2097150, F₂, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 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: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰⁹, 4194303, F₂, 4, 12) (dual of [(4194303, 4), 16777003, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²¹¹, 4194306, F₂, 4, 12) (dual of [(4194306, 4), 16777013, 13]-NRT-code)	[i]
3	Linear OOA(2²⁰⁸, 4194303, F₂, 4, 12) (dual of [(4194303, 4), 16777004, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁴⁴, 2097153, F₂, 5, 12) (dual of [(2097153, 5), 10485621, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(2¹⁴⁴, 2097153, F₂, 6, 12) (dual of [(2097153, 6), 12582774, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁴⁴, 2097153, F₂, 7, 12) (dual of [(2097153, 7), 14679927, 13]-NRT-code)	[i]
7	Linear OOA(2¹⁴⁴, 2097153, F₂, 8, 12) (dual of [(2097153, 8), 16777080, 13]-NRT-code)	[i]
8	Digital (132, 144, 2097153)-net over F₂	[i]