MinT - Information on Result #1061287

Information on Result #1061287

Linear OOA(3²⁴³, 2097151, F₃, 4, 25) (dual of [(2097151, 4), 8388361, 26]-NRT-code), using OOA 2-folding based on linear OOA(3²⁴³, 4194302, F₃, 2, 25) (dual of [(4194302, 2), 8388361, 26]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3²⁴¹, 4194301, F₃, 2, 25) (dual of [(4194301, 2), 8388361, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²⁴¹, 8388602, F₃, 25) (dual of [8388602, 8388361, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴¹, large, F₃, 25) (dual of [large, large−241, 26]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (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(3²⁴³, 2097151, F₃, 4, 24) (dual of [(2097151, 4), 8388361, 25]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²⁴⁷, 2097152, F₃, 4, 25) (dual of [(2097152, 4), 8388361, 26]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3²⁴⁴, 2097151, F₃, 4, 25) (dual of [(2097151, 4), 8388360, 26]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3²⁴⁵, 2097151, F₃, 4, 25) (dual of [(2097151, 4), 8388359, 26]-NRT-code)	[i]
5	Linear OOA(3²⁴⁶, 2097151, F₃, 4, 25) (dual of [(2097151, 4), 8388358, 26]-NRT-code)	[i]
6	Linear OOA(3²⁴³, 2088677, F₃, 5, 25) (dual of [(2088677, 5), 10443142, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
7	Digital (218, 243, 2088677)-net over F₃	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound