MinT - Information on Result #1060957

Information on Result #1060957

Linear OOA(3²¹³, 2097151, F₃, 4, 22) (dual of [(2097151, 4), 8388391, 23]-NRT-code), using OOA 2-folding based on linear OOA(3²¹³, 4194302, F₃, 2, 22) (dual of [(4194302, 2), 8388391, 23]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3²¹¹, 4194301, F₃, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²¹¹, 8388602, F₃, 22) (dual of [8388602, 8388391, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹¹, large, F₃, 22) (dual of [large, large−211, 23]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’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(3²¹³, 2097151, F₃, 4, 21) (dual of [(2097151, 4), 8388391, 22]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²¹⁷, 2097152, F₃, 4, 22) (dual of [(2097152, 4), 8388391, 23]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3²²¹, 2097153, F₃, 4, 22) (dual of [(2097153, 4), 8388391, 23]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
4	Linear OOA(3²¹⁴, 2097151, F₃, 4, 22) (dual of [(2097151, 4), 8388390, 23]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(3²¹⁵, 2097151, F₃, 4, 22) (dual of [(2097151, 4), 8388389, 23]-NRT-code)	[i]
6	Linear OOA(3²¹⁶, 2097151, F₃, 4, 22) (dual of [(2097151, 4), 8388388, 23]-NRT-code)	[i]
7	Linear OOA(3²⁴⁶, 2097235, F₃, 4, 22) (dual of [(2097235, 4), 8388694, 23]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
8	Linear OOA(3²⁴⁹, 2097265, F₃, 4, 22) (dual of [(2097265, 4), 8388811, 23]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
9	Linear OOA(3²¹³, 2097151, F₃, 5, 22) (dual of [(2097151, 5), 10485542, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
10	Digital (191, 213, 2097151)-net over F₃	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound