MinT - Information on Result #1051413

Information on Result #1051413

Linear OOA(2¹⁴⁰, 2097151, F₂, 4, 12) (dual of [(2097151, 4), 8388464, 13]-NRT-code), using OOA 2-folding 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: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁴², 2097151, F₂, 4, 12) (dual of [(2097151, 4), 8388462, 13]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁴³, 2097151, F₂, 4, 12) (dual of [(2097151, 4), 8388461, 13]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁶¹, 2097278, F₂, 4, 12) (dual of [(2097278, 4), 8388951, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
4	Linear OOA(2¹⁷⁴, 2099198, F₂, 4, 12) (dual of [(2099198, 4), 8396618, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁸⁰, 2105342, F₂, 4, 12) (dual of [(2105342, 4), 8421188, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁹², 2228222, F₂, 4, 12) (dual of [(2228222, 4), 8912696, 13]-NRT-code)	[i]
7	Linear OOA(2¹⁹⁸, 2621438, F₂, 4, 12) (dual of [(2621438, 4), 10485554, 13]-NRT-code)	[i]
8	Linear OOA(2²⁰⁷, 4194302, F₂, 4, 12) (dual of [(4194302, 4), 16777001, 13]-NRT-code)	[i]
9	Linear OOA(2¹⁶⁵, 2097405, F₂, 4, 12) (dual of [(2097405, 4), 8389455, 13]-NRT-code)	[i]
10	Linear OOA(2¹⁶⁸, 2097661, F₂, 4, 12) (dual of [(2097661, 4), 8390476, 13]-NRT-code)	[i]
11	Linear OOA(2¹⁷¹, 2098173, F₂, 4, 12) (dual of [(2098173, 4), 8392521, 13]-NRT-code)	[i]
12	Linear OOA(2¹⁷⁷, 2101245, F₂, 4, 12) (dual of [(2101245, 4), 8404803, 13]-NRT-code)	[i]
13	Linear OOA(2¹⁸³, 2113533, F₂, 4, 12) (dual of [(2113533, 4), 8453949, 13]-NRT-code)	[i]
14	Linear OOA(2¹⁸⁶, 2129917, F₂, 4, 12) (dual of [(2129917, 4), 8519482, 13]-NRT-code)	[i]
15	Linear OOA(2¹⁸⁹, 2162685, F₂, 4, 12) (dual of [(2162685, 4), 8650551, 13]-NRT-code)	[i]
16	Linear OOA(2¹⁹⁵, 2359293, F₂, 4, 12) (dual of [(2359293, 4), 9436977, 13]-NRT-code)	[i]
17	Linear OOA(2²⁰¹, 3145725, F₂, 4, 12) (dual of [(3145725, 4), 12582699, 13]-NRT-code)	[i]
18	Linear OOA(2²⁰⁴, 4194301, F₂, 4, 12) (dual of [(4194301, 4), 16777000, 13]-NRT-code)	[i]
19	Linear OOA(2¹⁴⁰, 2097151, F₂, 5, 12) (dual of [(2097151, 5), 10485615, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
20	Linear OOA(2¹⁴⁰, 2097151, F₂, 6, 12) (dual of [(2097151, 6), 12582766, 13]-NRT-code)	[i]
21	Linear OOA(2¹⁴⁰, 2097151, F₂, 7, 12) (dual of [(2097151, 7), 14679917, 13]-NRT-code)	[i]
22	Linear OOA(2¹⁴⁰, 2097151, F₂, 8, 12) (dual of [(2097151, 8), 16777068, 13]-NRT-code)	[i]
23	Digital (128, 140, 2097151)-net over F₂	[i]