MinT - Information on Result #1021167

Information on Result #1021167

Linear OOA(3⁹⁴, 5778089, F₃, 3, 7) (dual of [(5778089, 3), 17334173, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3¹⁴, 1490944, F₃, 3, 2) (dual of [(1490944, 3), 4472818, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁴, 2391484, F₃, 3, 2) (dual of [(2391484, 3), 7174438, 3]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(3¹⁴, 2391484, F₃, 2, 2) (dual of [(2391484, 2), 4782954, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(3¹⁴, 2391484, F₃, 2) (dual of [2391484, 2391470, 3]-code), using
      - Hamming code H(14,3) [i]
linear OOA(3¹⁹, 1490944, F₃, 3, 3) (dual of [(1490944, 3), 4472813, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(3¹⁹, 1490944, F₃, 2, 3) (dual of [(1490944, 2), 2981869, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3¹⁹, 1490944, F₃, 3) (dual of [1490944, 1490925, 4]-code or 1490944-cap in PG(18,3)), using
    - doubling the cap [i] based on linear OA(3¹⁸, 745472, F₃, 3) (dual of [745472, 745454, 4]-code or 745472-cap in PG(17,3)), 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.

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

None.