MinT - Information on Result #1117827

Information on Result #1117827

Linear OOA(3²³⁷, 1682645, F₃, 5, 19) (dual of [(1682645, 5), 8412988, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁵⁶, 4925, F₃, 5, 9) (dual of [(4925, 5), 24569, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3⁵⁶, 19701, F₃, 9) (dual of [19701, 19645, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁵⁶, 19703, F₃, 9) (dual of [19703, 19647, 10]-code), using
    - constructionÂ X applied to C([0,4]) âŠ‚ C([0,3]) [i] based on
      1. linear OA(3⁵⁵, 19684, F₃, 9) (dual of [19684, 19629, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
      2. linear OA(3³⁷, 19684, F₃, 7) (dual of [19684, 19647, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      3. linear OA(3¹, 19, F₃, 1) (dual of [19, 18, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OOA(3¹⁸¹, 1677720, F₃, 5, 19) (dual of [(1677720, 5), 8388419, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁸¹, 8388600, F₃, 19) (dual of [8388600, 8388419, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (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.