MinT - Information on Result #1466341

Information on Result #1466341

Linear OOA(3¹³⁷, 4194366, F₃, 2, 13) (dual of [(4194366, 2), 8388595, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁶, 65, F₃, 2, 6) (dual of [(65, 2), 114, 7]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹⁶, 65, F₃, 6) (dual of [65, 49, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁶, 80, F₃, 6) (dual of [80, 64, 7]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [1,5], 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(3¹³⁷, 4194366, F₃, 3, 13) (dual of [(4194366, 3), 12582961, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹³⁷, 4194366, F₃, 4, 13) (dual of [(4194366, 4), 16777327, 14]-NRT-code)	[i]
3	Linear OOA(3¹³⁷, 4194366, F₃, 5, 13) (dual of [(4194366, 5), 20971693, 14]-NRT-code)	[i]
4	Digital (124, 137, 4194366)-net over F₃	[i]