MinT - Information on Result #864974

Information on Result #864974

Linear OOA(27²⁶, 4194301, F₂₇, 2, 6) (dual of [(4194301, 2), 8388576, 7]-NRT-code), using OOA 2-folding based on linear OA(27²⁶, 8388602, F₂₇, 6) (dual of [8388602, 8388576, 7]-code), using

discarding factors / shortening the dual code based on linear OA(27²⁶, large, F₂₇, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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(27²⁸, 4194302, F₂₇, 2, 6) (dual of [(4194302, 2), 8388576, 7]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(27²⁷, 4194301, F₂₇, 2, 6) (dual of [(4194301, 2), 8388575, 7]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3⁷⁸, large, F₃, 2, 6)	[i]	Trace Code for OOAs
4	Linear OOA(27²⁹, 4194329, F₂₇, 2, 6) (dual of [(4194329, 2), 8388629, 7]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
5	Linear OOA(27³⁰, 4195031, F₂₇, 2, 6) (dual of [(4195031, 2), 8390032, 7]-NRT-code)	[i]
6	Linear OOA(27³¹, 4196009, F₂₇, 2, 6) (dual of [(4196009, 2), 8391987, 7]-NRT-code)	[i]
7	Linear OOA(27³², 4214797, F₂₇, 2, 6) (dual of [(4214797, 2), 8429562, 7]-NRT-code)	[i]
8	Linear OOA(27³³, 4727200, F₂₇, 2, 6) (dual of [(4727200, 2), 9454367, 7]-NRT-code)	[i]
9	Linear OOA(27³⁴, 5439434, F₂₇, 2, 6) (dual of [(5439434, 2), 10878834, 7]-NRT-code)	[i]
10	Linear OOA(27³⁵, 8388602, F₂₇, 2, 6) (dual of [(8388602, 2), 16777169, 7]-NRT-code)	[i]
11	Linear OOA(27⁸², 8388602, F₂₇, 2, 12) (dual of [(8388602, 2), 16777122, 13]-NRT-code)	[i]
12	Linear OOA(27⁸⁷, 8388602, F₂₇, 2, 13) (dual of [(8388602, 2), 16777117, 14]-NRT-code)	[i]