MinT - Information on Result #1059786

Information on Result #1059786

Linear OOA(3¹⁶², 4194301, F₃, 4, 12) (dual of [(4194301, 4), 16777042, 13]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁶², 8388602, F₃, 2, 12) (dual of [(8388602, 2), 16777042, 13]-NRT-code), using

trace code [i] based on linear OOA(9⁸¹, 4194301, F₉, 2, 12) (dual of [(4194301, 2), 8388521, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9⁸¹, 8388602, F₉, 12) (dual of [8388602, 8388521, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁸¹, large, F₉, 12) (dual of [large, large−81, 13]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 9⁸âˆ’1, defining interval IÂ =Â [0,11], 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(3¹⁶⁶, 4194302, F₃, 4, 12) (dual of [(4194302, 4), 16777042, 13]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3¹⁶³, 4194301, F₃, 4, 12) (dual of [(4194301, 4), 16777041, 13]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3¹⁶⁴, 4194301, F₃, 4, 12) (dual of [(4194301, 4), 16777040, 13]-NRT-code)	[i]
4	Linear OOA(3¹⁶⁵, 4194301, F₃, 4, 12) (dual of [(4194301, 4), 16777039, 13]-NRT-code)	[i]
5	Linear OOA(3¹⁶⁸, 4194305, F₃, 4, 12) (dual of [(4194305, 4), 16777052, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
6	Linear OOA(3¹⁶⁹, 4194308, F₃, 4, 12) (dual of [(4194308, 4), 16777063, 13]-NRT-code)	[i]
7	Linear OOA(3¹⁷⁰, 4194310, F₃, 4, 12) (dual of [(4194310, 4), 16777070, 13]-NRT-code)	[i]
8	Linear OOA(3¹⁷¹, 4194314, F₃, 4, 12) (dual of [(4194314, 4), 16777085, 13]-NRT-code)	[i]
9	Linear OOA(3¹⁷², 4194320, F₃, 4, 12) (dual of [(4194320, 4), 16777108, 13]-NRT-code)	[i]
10	Linear OOA(3¹⁷³, 4194326, F₃, 4, 12) (dual of [(4194326, 4), 16777131, 13]-NRT-code)	[i]
11	Linear OOA(3¹⁷⁴, 4194334, F₃, 4, 12) (dual of [(4194334, 4), 16777162, 13]-NRT-code)	[i]
12	Linear OOA(3¹⁷⁵, 4194343, F₃, 4, 12) (dual of [(4194343, 4), 16777197, 13]-NRT-code)	[i]
13	Linear OOA(3¹⁷⁸, 4194347, F₃, 4, 12) (dual of [(4194347, 4), 16777210, 13]-NRT-code)	[i]
14	Linear OOA(3¹⁷⁹, 4194354, F₃, 4, 12) (dual of [(4194354, 4), 16777237, 13]-NRT-code)	[i]