MinT - Information on Result #2522990

Information on Result #2522990

Linear OOA(256⁵⁷, 4194302, F₂₅₆, 2, 19) (dual of [(4194302, 2), 8388547, 20]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(256⁵⁵, 4194301, F₂₅₆, 2, 19) (dual of [(4194301, 2), 8388547, 20]-NRT-code), using

OOA 2-folding [i] based on linear OA(256⁵⁵, 8388602, F₂₅₆, 19) (dual of [8388602, 8388547, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(256⁵⁵, large, F₂₅₆, 19) (dual of [large, large−55, 20]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(256⁵⁸, 4194302, F₂₅₆, 2, 19) (dual of [(4194302, 2), 8388546, 20]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(256⁵⁷, 4194302, F₂₅₆, 3, 19) (dual of [(4194302, 3), 12582849, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(256⁵⁷, 4194302, F₂₅₆, 4, 19) (dual of [(4194302, 4), 16777151, 20]-NRT-code)	[i]
4	Linear OOA(256⁵⁷, 4194302, F₂₅₆, 5, 19) (dual of [(4194302, 5), 20971453, 20]-NRT-code)	[i]
5	Linear OOA(256⁵⁷, 4194302, F₂₅₆, 6, 19) (dual of [(4194302, 6), 25165755, 20]-NRT-code)	[i]
6	Digital (38, 57, 4194302)-net over F₂₅₆	[i]
7	Linear OOA(256⁵⁷, 2097151, F₂₅₆, 4, 19) (dual of [(2097151, 4), 8388547, 20]-NRT-code)	[i]	OOA Folding