MinT - Information on Result #2485695

Information on Result #2485695

Linear OOA(3¹²⁴, 4194303, F₃, 2, 12) (dual of [(4194303, 2), 8388482, 13]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(3¹²⁰, 4194301, F₃, 2, 12) (dual of [(4194301, 2), 8388482, 13]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹²⁰, 8388602, F₃, 12) (dual of [8388602, 8388482, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹²⁰, large, F₃, 12) (dual of [large, large−120, 13]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(3¹²⁵, 4194303, F₃, 2, 12) (dual of [(4194303, 2), 8388481, 13]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹²⁴, 4194303, F₃, 3, 12) (dual of [(4194303, 3), 12582785, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3¹²⁴, 4194303, F₃, 4, 12) (dual of [(4194303, 4), 16777088, 13]-NRT-code)	[i]
4	Linear OOA(3¹²⁴, 4194303, F₃, 5, 12) (dual of [(4194303, 5), 20971391, 13]-NRT-code)	[i]
5	Digital (112, 124, 4194303)-net over F₃	[i]