MinT - Information on Result #1060587

Information on Result #1060587

Linear OOA(3¹⁸³, 2097151, F₃, 4, 19) (dual of [(2097151, 4), 8388421, 20]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁸³, 4194302, F₃, 2, 19) (dual of [(4194302, 2), 8388421, 20]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁸¹, 4194301, F₃, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁸¹, 8388602, F₃, 19) (dual of [8388602, 8388421, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (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(3¹⁸³, 2097151, F₃, 4, 18) (dual of [(2097151, 4), 8388421, 19]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁸⁷, 2097152, F₃, 4, 19) (dual of [(2097152, 4), 8388421, 20]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3¹⁸⁴, 2097151, F₃, 4, 19) (dual of [(2097151, 4), 8388420, 20]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3¹⁸⁵, 2097151, F₃, 4, 19) (dual of [(2097151, 4), 8388419, 20]-NRT-code)	[i]
5	Linear OOA(3¹⁸⁶, 2097151, F₃, 4, 19) (dual of [(2097151, 4), 8388418, 20]-NRT-code)	[i]
6	Linear OOA(3²¹⁰, 2097235, F₃, 4, 19) (dual of [(2097235, 4), 8388730, 20]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
7	Linear OOA(3²¹³, 2097265, F₃, 4, 19) (dual of [(2097265, 4), 8388847, 20]-NRT-code)	[i]
8	Linear OOA(3²¹⁹, 2097479, F₃, 4, 19) (dual of [(2097479, 4), 8389697, 20]-NRT-code)	[i]
9	Linear OOA(3¹⁸³, 2097151, F₃, 5, 19) (dual of [(2097151, 5), 10485572, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
10	Digital (164, 183, 2097151)-net over F₃	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound