MinT - Information on Result #2675738

Information on Result #2675738

Linear OOA(3¹²⁹, large, F₃, 3, 7), using 11 times NRT-code embedding in larger space based on linear OOA(3⁹⁶, large, F₃, 3, 7), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁵, 2796201, F₃, 3, 2) (dual of [(2796201, 3), 8388588, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹⁵, 7174453, F₃, 3, 2) (dual of [(7174453, 3), 21523344, 3]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(3¹⁵, 7174453, F₃, 2, 2) (dual of [(7174453, 2), 14348891, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(3¹⁵, 7174453, F₃, 2) (dual of [7174453, 7174438, 3]-code), using
        Hamming code H(15,3) [i]
2. 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]
3. 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.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹³⁰, large, F₃, 3, 7)	[i]		OOA Duplication
2	Linear OOA(3¹³¹, large, F₃, 3, 7)	[i]		OOA Duplication