MinT - Information on Result #2523015

Information on Result #2523015

Linear OOA(256⁶⁷, 4194302, F₂₅₆, 2, 22) (dual of [(4194302, 2), 8388537, 23]-NRT-code), using 256¹ times duplication based on linear OOA(256⁶⁶, 4194302, F₂₅₆, 2, 22) (dual of [(4194302, 2), 8388538, 23]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(256⁶⁴, 4194301, F₂₅₆, 2, 22) (dual of [(4194301, 2), 8388538, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256⁶⁴, 8388602, F₂₅₆, 22) (dual of [8388602, 8388538, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁶⁴, large, F₂₅₆, 22) (dual of [large, large−64, 23]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(256⁶⁷, 4194302, F₂₅₆, 3, 22) (dual of [(4194302, 3), 12582839, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁶⁷, 4194302, F₂₅₆, 4, 22) (dual of [(4194302, 4), 16777141, 23]-NRT-code)	[i]
3	Linear OOA(256⁶⁷, 4194302, F₂₅₆, 5, 22) (dual of [(4194302, 5), 20971443, 23]-NRT-code)	[i]
4	Linear OOA(256⁶⁷, 4194302, F₂₅₆, 6, 22) (dual of [(4194302, 6), 25165745, 23]-NRT-code)	[i]
5	Digital (45, 67, 4194302)-net over F₂₅₆	[i]