MinT - Information on Result #874004

Information on Result #874004

Linear OOA(64⁶¹, 4194301, F₆₄, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using OOA 2-folding based on linear OA(64⁶¹, 8388602, F₆₄, 16) (dual of [8388602, 8388541, 17]-code), using

discarding factors / shortening the dual code based on linear OA(64⁶¹, large, F₆₄, 16) (dual of [large, large−61, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(64⁶³, 4194302, F₆₄, 2, 16) (dual of [(4194302, 2), 8388541, 17]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(64⁶⁵, 4194303, F₆₄, 2, 16) (dual of [(4194303, 2), 8388541, 17]-NRT-code)	[i]
3	Linear OOA(64⁶⁷, 4194304, F₆₄, 2, 16) (dual of [(4194304, 2), 8388541, 17]-NRT-code)	[i]
4	Linear OOA(64⁶², 4194301, F₆₄, 2, 16) (dual of [(4194301, 2), 8388540, 17]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(8¹²², 8388602, F₈, 2, 16) (dual of [(8388602, 2), 16777082, 17]-NRT-code)	[i]	Trace Code for OOAs
6	Linear OOA(64⁶⁹, 4194366, F₆₄, 2, 16) (dual of [(4194366, 2), 8388663, 17]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
7	Linear OOA(64⁷⁰, 4194381, F₆₄, 2, 16) (dual of [(4194381, 2), 8388692, 17]-NRT-code)	[i]
8	Linear OOA(64⁷², 4194405, F₆₄, 2, 16) (dual of [(4194405, 2), 8388738, 17]-NRT-code)	[i]
9	Linear OOA(64⁷³, 4194431, F₆₄, 2, 16) (dual of [(4194431, 2), 8388789, 17]-NRT-code)	[i]
10	Linear OOA(64⁷⁴, 4194446, F₆₄, 2, 16) (dual of [(4194446, 2), 8388818, 17]-NRT-code)	[i]
11	Linear OOA(64⁷⁵, 4194528, F₆₄, 2, 16) (dual of [(4194528, 2), 8388981, 17]-NRT-code)	[i]
12	Linear OOA(64⁷⁶, 4196350, F₆₄, 2, 16) (dual of [(4196350, 2), 8392624, 17]-NRT-code)	[i]
13	Linear OOA(64⁷⁷, 4196351, F₆₄, 2, 16) (dual of [(4196351, 2), 8392625, 17]-NRT-code)	[i]
14	Linear OOA(64⁷⁸, 4196353, F₆₄, 2, 16) (dual of [(4196353, 2), 8392628, 17]-NRT-code)	[i]
15	Linear OOA(64⁷⁹, 4196354, F₆₄, 2, 16) (dual of [(4196354, 2), 8392629, 17]-NRT-code)	[i]
16	Linear OOA(64⁸⁰, 4196415, F₆₄, 2, 16) (dual of [(4196415, 2), 8392750, 17]-NRT-code)	[i]
17	Linear OOA(64⁸¹, 4196430, F₆₄, 2, 16) (dual of [(4196430, 2), 8392779, 17]-NRT-code)	[i]
18	Linear OOA(64⁸², 4199155, F₆₄, 2, 16) (dual of [(4199155, 2), 8398228, 17]-NRT-code)	[i]
19	Linear OOA(64⁸³, 4325374, F₆₄, 2, 16) (dual of [(4325374, 2), 8650665, 17]-NRT-code)	[i]
20	Linear OOA(64⁸⁴, 4325376, F₆₄, 2, 16) (dual of [(4325376, 2), 8650668, 17]-NRT-code)	[i]
21	Linear OOA(64⁸⁵, 4325378, F₆₄, 2, 16) (dual of [(4325378, 2), 8650671, 17]-NRT-code)	[i]
22	Linear OOA(64⁸⁶, 4325380, F₆₄, 2, 16) (dual of [(4325380, 2), 8650674, 17]-NRT-code)	[i]
23	Linear OOA(64⁸⁷, 4325439, F₆₄, 2, 16) (dual of [(4325439, 2), 8650791, 17]-NRT-code)	[i]
24	Linear OOA(64⁸⁸, 4325454, F₆₄, 2, 16) (dual of [(4325454, 2), 8650820, 17]-NRT-code)	[i]
25	Linear OOA(64⁸⁹, 4327390, F₆₄, 2, 16) (dual of [(4327390, 2), 8654691, 17]-NRT-code)	[i]
26	Linear OOA(64⁹⁰, 8388602, F₆₄, 2, 16) (dual of [(8388602, 2), 16777114, 17]-NRT-code)	[i]
27	Linear OOA(64⁸¹, 4198461, F₆₄, 2, 16) (dual of [(4198461, 2), 8396841, 17]-NRT-code)	[i]
28	OOA(64⁷¹, 4194430, S₆₄, 2, 16)	[i]
29	OOA(64⁷², 4194558, S₆₄, 2, 16)	[i]
30	OOA(64⁷³, 4194559, S₆₄, 2, 16)	[i]
31	OOA(64⁷⁹, 4202494, S₆₄, 2, 16)	[i]
32	OOA(64⁸⁰, 4202495, S₆₄, 2, 16)	[i]
33	OOA(64⁸¹, 4227070, S₆₄, 2, 16)	[i]
34	OOA(64⁸⁷, 5242878, S₆₄, 2, 16)	[i]
35	OOA(64⁸⁸, 5242880, S₆₄, 2, 16)	[i]
36	OOA(64⁸⁹, 5242882, S₆₄, 2, 16)	[i]