MinT - Information on Result #1119287

Information on Result #1119287

Linear OOA(3²²¹, 3355478, F₃, 5, 15) (dual of [(3355478, 5), 16777169, 16]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3¹⁰, 38, F₃, 5, 5) (dual of [(38, 5), 180, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3¹⁰, 38, F₃, 4, 5) (dual of [(38, 4), 142, 6]-NRT-code), using
  - extracting embedded OOA [i] based on digital (5, 10, 38)-net over F₃, using
    - linear code embedding found in a computer search [i]
linear OOA(3⁶¹, 1677720, F₃, 5, 7) (dual of [(1677720, 5), 8388539, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁶¹, 2796200, F₃, 5, 7) (dual of [(2796200, 5), 13980939, 8]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OA(3⁶¹, 8388601, F₃, 7) (dual of [8388601, 8388540, 8]-code), using
    - discarding factors / shortening the dual code 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]
linear OOA(3¹⁵⁰, 1677720, F₃, 5, 15) (dual of [(1677720, 5), 8388450, 16]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁵⁰, 8388600, F₃, 15) (dual of [8388600, 8388450, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.