MinT - Information on Result #1466345

Information on Result #1466345

Linear OOA(3¹⁴¹, 4194502, F₃, 2, 13) (dual of [(4194502, 2), 8388863, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁰, 201, F₃, 2, 6) (dual of [(201, 2), 382, 7]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁰, 201, F₃, 6) (dual of [201, 181, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁰, 242, F₃, 6) (dual of [242, 222, 7]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(3¹²¹, 4194301, F₃, 2, 13) (dual of [(4194301, 2), 8388481, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹²¹, 8388602, F₃, 13) (dual of [8388602, 8388481, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁴¹, 4194502, F₃, 3, 13) (dual of [(4194502, 3), 12583365, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁴¹, 4194502, F₃, 4, 13) (dual of [(4194502, 4), 16777867, 14]-NRT-code)	[i]
3	Linear OOA(3¹⁴¹, 4194502, F₃, 5, 13) (dual of [(4194502, 5), 20972369, 14]-NRT-code)	[i]
4	Digital (128, 141, 4194502)-net over F₃	[i]
5	Linear OOA(3¹⁴¹, 2097251, F₃, 4, 13) (dual of [(2097251, 4), 8388863, 14]-NRT-code)	[i]	OOA Folding