MinT - Information on Result #1051624

Information on Result #1051624

Linear OOA(2¹⁶³, 2097151, F₂, 4, 14) (dual of [(2097151, 4), 8388441, 15]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁶³, 4194302, F₂, 2, 14) (dual of [(4194302, 2), 8388441, 15]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁶¹, 4194301, F₂, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁶¹, 8388602, F₂, 14) (dual of [8388602, 8388441, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(2¹⁶⁷, 2097152, F₂, 4, 14) (dual of [(2097152, 4), 8388441, 15]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁶⁵, 2097151, F₂, 4, 14) (dual of [(2097151, 4), 8388439, 15]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁶⁶, 2097151, F₂, 4, 14) (dual of [(2097151, 4), 8388438, 15]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2¹⁸⁶, 2097278, F₂, 4, 14) (dual of [(2097278, 4), 8388926, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
5	Linear OOA(2¹⁸⁹, 2097405, F₂, 4, 14) (dual of [(2097405, 4), 8389431, 15]-NRT-code)	[i]
6	Linear OOA(2¹⁹², 2097661, F₂, 4, 14) (dual of [(2097661, 4), 8390452, 15]-NRT-code)	[i]
7	Linear OOA(2¹⁹⁵, 2098173, F₂, 4, 14) (dual of [(2098173, 4), 8392497, 15]-NRT-code)	[i]
8	Linear OOA(2¹⁹⁸, 2099198, F₂, 4, 14) (dual of [(2099198, 4), 8396594, 15]-NRT-code)	[i]
9	Linear OOA(2²⁰¹, 2101245, F₂, 4, 14) (dual of [(2101245, 4), 8404779, 15]-NRT-code)	[i]
10	Linear OOA(2²⁰⁴, 2105342, F₂, 4, 14) (dual of [(2105342, 4), 8421164, 15]-NRT-code)	[i]
11	Linear OOA(2²⁰⁷, 2113533, F₂, 4, 14) (dual of [(2113533, 4), 8453925, 15]-NRT-code)	[i]
12	Linear OOA(2²¹⁰, 2129917, F₂, 4, 14) (dual of [(2129917, 4), 8519458, 15]-NRT-code)	[i]
13	Linear OOA(2²¹³, 2162685, F₂, 4, 14) (dual of [(2162685, 4), 8650527, 15]-NRT-code)	[i]
14	Linear OOA(2²¹⁶, 2228222, F₂, 4, 14) (dual of [(2228222, 4), 8912672, 15]-NRT-code)	[i]
15	Linear OOA(2²¹⁹, 2359293, F₂, 4, 14) (dual of [(2359293, 4), 9436953, 15]-NRT-code)	[i]
16	Linear OOA(2²²², 2621438, F₂, 4, 14) (dual of [(2621438, 4), 10485530, 15]-NRT-code)	[i]
17	Linear OOA(2²²⁵, 3145725, F₂, 4, 14) (dual of [(3145725, 4), 12582675, 15]-NRT-code)	[i]
18	Linear OOA(2²²⁸, 4194301, F₂, 4, 14) (dual of [(4194301, 4), 16776976, 15]-NRT-code)	[i]
19	Linear OOA(2²³¹, 4194302, F₂, 4, 14) (dual of [(4194302, 4), 16776977, 15]-NRT-code)	[i]
20	Linear OOA(2¹⁸⁹, 2097406, F₂, 4, 14) (dual of [(2097406, 4), 8389435, 15]-NRT-code)	[i]