MinT - Information on Result #873965

Information on Result #873965

Linear OOA(64⁵⁷, 4194301, F₆₄, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using OOA 2-folding based on linear OA(64⁵⁷, 8388602, F₆₄, 15) (dual of [8388602, 8388545, 16]-code), using

discarding factors / shortening the dual code based on linear OA(64⁵⁷, large, F₆₄, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [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(64⁵⁹, 4194302, F₆₄, 2, 15) (dual of [(4194302, 2), 8388545, 16]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(64⁶¹, 4194303, F₆₄, 2, 15) (dual of [(4194303, 2), 8388545, 16]-NRT-code)	[i]
3	Linear OOA(64⁶³, 4194304, F₆₄, 2, 15) (dual of [(4194304, 2), 8388545, 16]-NRT-code)	[i]
4	Linear OOA(64⁵⁸, 4194301, F₆₄, 2, 15) (dual of [(4194301, 2), 8388544, 16]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(4¹⁷¹, large, F₄, 2, 15)	[i]	Trace Code for OOAs
6	Linear OOA(8¹¹⁴, 8388602, F₈, 2, 15) (dual of [(8388602, 2), 16777090, 16]-NRT-code)	[i]	Trace Code for OOAs
7	Linear OOA(64⁶⁴, 4194366, F₆₄, 2, 15) (dual of [(4194366, 2), 8388668, 16]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
8	Linear OOA(64⁶⁵, 4194381, F₆₄, 2, 15) (dual of [(4194381, 2), 8388697, 16]-NRT-code)	[i]
9	Linear OOA(64⁶⁷, 4194431, F₆₄, 2, 15) (dual of [(4194431, 2), 8388795, 16]-NRT-code)	[i]
10	Linear OOA(64⁶⁸, 4194446, F₆₄, 2, 15) (dual of [(4194446, 2), 8388824, 16]-NRT-code)	[i]
11	Linear OOA(64⁶⁹, 4194461, F₆₄, 2, 15) (dual of [(4194461, 2), 8388853, 16]-NRT-code)	[i]
12	Linear OOA(64⁷⁰, 4196350, F₆₄, 2, 15) (dual of [(4196350, 2), 8392630, 16]-NRT-code)	[i]
13	Linear OOA(64⁷¹, 4196352, F₆₄, 2, 15) (dual of [(4196352, 2), 8392633, 16]-NRT-code)	[i]
14	Linear OOA(64⁷², 4196353, F₆₄, 2, 15) (dual of [(4196353, 2), 8392634, 16]-NRT-code)	[i]
15	Linear OOA(64⁷³, 4196415, F₆₄, 2, 15) (dual of [(4196415, 2), 8392757, 16]-NRT-code)	[i]
16	Linear OOA(64⁷⁴, 4198399, F₆₄, 2, 15) (dual of [(4198399, 2), 8396724, 16]-NRT-code)	[i]
17	Linear OOA(64⁷⁵, 4198403, F₆₄, 2, 15) (dual of [(4198403, 2), 8396731, 16]-NRT-code)	[i]
18	Linear OOA(64⁷⁶, 4325374, F₆₄, 2, 15) (dual of [(4325374, 2), 8650672, 16]-NRT-code)	[i]
19	Linear OOA(64⁷⁷, 4325377, F₆₄, 2, 15) (dual of [(4325377, 2), 8650677, 16]-NRT-code)	[i]
20	Linear OOA(64⁷⁸, 4325378, F₆₄, 2, 15) (dual of [(4325378, 2), 8650678, 16]-NRT-code)	[i]
21	Linear OOA(64⁷⁹, 4325439, F₆₄, 2, 15) (dual of [(4325439, 2), 8650799, 16]-NRT-code)	[i]
22	Linear OOA(64⁸⁰, 4329471, F₆₄, 2, 15) (dual of [(4329471, 2), 8658862, 16]-NRT-code)	[i]
23	Linear OOA(64⁸¹, 4333639, F₆₄, 2, 15) (dual of [(4333639, 2), 8667197, 16]-NRT-code)	[i]
24	Linear OOA(64⁸², 8388602, F₆₄, 2, 15) (dual of [(8388602, 2), 16777122, 16]-NRT-code)	[i]
25	Linear OOA(64⁶⁹, 4194496, F₆₄, 2, 15) (dual of [(4194496, 2), 8388923, 16]-NRT-code)	[i]
26	Linear OOA(64⁷³, 4198461, F₆₄, 2, 15) (dual of [(4198461, 2), 8396849, 16]-NRT-code)	[i]
27	Linear OOA(64⁷⁴, 4198476, F₆₄, 2, 15) (dual of [(4198476, 2), 8396878, 16]-NRT-code)	[i]
28	Linear OOA(64⁷⁵, 4198491, F₆₄, 2, 15) (dual of [(4198491, 2), 8396907, 16]-NRT-code)	[i]
29	OOA(64⁶⁶, 4194430, S₆₄, 2, 15)	[i]
30	OOA(64⁶⁷, 4194558, S₆₄, 2, 15)	[i]
31	OOA(64⁶⁸, 4194559, S₆₄, 2, 15)	[i]
32	OOA(64⁶⁹, 4194560, S₆₄, 2, 15)	[i]
33	OOA(64⁷³, 4202494, S₆₄, 2, 15)	[i]
34	OOA(64⁷⁴, 4202496, S₆₄, 2, 15)	[i]
35	OOA(64⁷⁵, 4227070, S₆₄, 2, 15)	[i]
36	OOA(64⁸⁰, 5242878, S₆₄, 2, 15)	[i]
37	OOA(64⁸¹, 5242881, S₆₄, 2, 15)	[i]