MinT - Information on Result #1021178

Information on Result #1021178

Linear OOA(3⁹³, 5858122, F₃, 3, 7) (dual of [(5858122, 3), 17574273, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3¹², 265720, F₃, 3, 2) (dual of [(265720, 3), 797148, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(3¹², 265720, F₃, 2, 2) (dual of [(265720, 2), 531428, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(3¹², 265720, F₃, 2) (dual of [265720, 265708, 3]-code), using
    - Hamming code H(12,3) [i]
linear OOA(3²⁰, 2796201, F₃, 3, 3) (dual of [(2796201, 3), 8388583, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁰, 3713023, F₃, 3, 3) (dual of [(3713023, 3), 11139049, 4]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OA(3²⁰, 3713024, F₃, 3) (dual of [3713024, 3713004, 4]-code or 3713024-cap in PG(19,3)), using
    - large caps in PG(u,Â 3) [i]
linear OOA(3⁶¹, 2796201, F₃, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3⁹³, 5858121, F₃, 4, 7) (dual of [(5858121, 4), 23432391, 8]-NRT-code)	[i]	OOA Stacking with Additional Row
2	Linear OOA(3⁹³, 5858121, F₃, 5, 7) (dual of [(5858121, 5), 29290512, 8]-NRT-code)	[i]
3	Linear OOA(3⁹³, 5858121, F₃, 9, 7) (dual of [(5858121, 9), 52722996, 8]-NRT-code)	[i]