MinT - Information on Result #873755

Information on Result #873755

Linear OOA(64²⁵, 4194301, F₆₄, 2, 7) (dual of [(4194301, 2), 8388577, 8]-NRT-code), using OOA 2-folding based on linear OA(64²⁵, 8388602, F₆₄, 7) (dual of [8388602, 8388577, 8]-code), using

discarding factors / shortening the dual code based on linear OA(64²⁵, large, F₆₄, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (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(64²⁷, 4194302, F₆₄, 2, 7) (dual of [(4194302, 2), 8388577, 8]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(64²⁶, 4194301, F₆₄, 2, 7) (dual of [(4194301, 2), 8388576, 8]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(4⁷⁵, large, F₄, 2, 7)	[i]	Trace Code for OOAs
4	Linear OOA(8⁵⁰, 8388602, F₈, 2, 7) (dual of [(8388602, 2), 16777154, 8]-NRT-code)	[i]	Trace Code for OOAs
5	Linear OOA(64²⁸, 4194366, F₆₄, 2, 7) (dual of [(4194366, 2), 8388704, 8]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
6	Linear OOA(64²⁹, 4198398, F₆₄, 2, 7) (dual of [(4198398, 2), 8396767, 8]-NRT-code)	[i]
7	Linear OOA(64³⁰, 4202566, F₆₄, 2, 7) (dual of [(4202566, 2), 8405102, 8]-NRT-code)	[i]
8	Linear OOA(64³¹, 4464703, F₆₄, 2, 7) (dual of [(4464703, 2), 8929375, 8]-NRT-code)	[i]
9	Linear OOA(64³², 8388602, F₆₄, 2, 7) (dual of [(8388602, 2), 16777172, 8]-NRT-code)	[i]
10	Linear OOA(64⁷⁸, 8388602, F₆₄, 2, 14) (dual of [(8388602, 2), 16777126, 15]-NRT-code)	[i]
11	Linear OOA(64⁸², 8388602, F₆₄, 2, 15) (dual of [(8388602, 2), 16777122, 16]-NRT-code)	[i]
12	OOA(64³⁰, 4210685, S₆₄, 2, 7)	[i]
13	OOA(64³⁰, 4210686, S₆₄, 2, 7)	[i]