MinT - Information on Result #864995

Information on Result #864995

Linear OOA(27³¹, 4194301, F₂₇, 2, 7) (dual of [(4194301, 2), 8388571, 8]-NRT-code), using OOA 2-folding based on linear OA(27³¹, 8388602, F₂₇, 7) (dual of [8388602, 8388571, 8]-code), using

discarding factors / shortening the dual code based on linear OA(27³¹, large, F₂₇, 7) (dual of [large, large−31, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’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(27³³, 4194302, F₂₇, 2, 7) (dual of [(4194302, 2), 8388571, 8]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(27³², 4194301, F₂₇, 2, 7) (dual of [(4194301, 2), 8388570, 8]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3⁹³, large, F₃, 2, 7)	[i]	Trace Code for OOAs
4	Linear OOA(27³⁴, 4194329, F₂₇, 2, 7) (dual of [(4194329, 2), 8388624, 8]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
5	Linear OOA(27³⁵, 4195031, F₂₇, 2, 7) (dual of [(4195031, 2), 8390027, 8]-NRT-code)	[i]
6	Linear OOA(27³⁶, 4196009, F₂₇, 2, 7) (dual of [(4196009, 2), 8391982, 8]-NRT-code)	[i]
7	Linear OOA(27³⁷, 4214797, F₂₇, 2, 7) (dual of [(4214797, 2), 8429557, 8]-NRT-code)	[i]
8	Linear OOA(27³⁸, 4727200, F₂₇, 2, 7) (dual of [(4727200, 2), 9454362, 8]-NRT-code)	[i]
9	Linear OOA(27³⁹, 5439434, F₂₇, 2, 7) (dual of [(5439434, 2), 10878829, 8]-NRT-code)	[i]
10	Linear OOA(27⁴⁰, 8388602, F₂₇, 2, 7) (dual of [(8388602, 2), 16777164, 8]-NRT-code)	[i]
11	Linear OOA(27⁹⁷, 8388602, F₂₇, 2, 14) (dual of [(8388602, 2), 16777107, 15]-NRT-code)	[i]
12	Linear OOA(27¹⁰², 8388602, F₂₇, 2, 15) (dual of [(8388602, 2), 16777102, 16]-NRT-code)	[i]