MinT - Information on Result #1119269

Information on Result #1119269

Linear OOA(3²⁵⁰, 3355458, F₃, 5, 17) (dual of [(3355458, 5), 16777040, 18]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁸, 18, F₃, 5, 5) (dual of [(18, 5), 82, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3⁸, 18, F₃, 4, 5) (dual of [(18, 4), 64, 6]-NRT-code), using
  - extracting embedded OOA [i] based on digital (3, 8, 18)-net over F₃, using
    - linear code embedding found in a computer search [i]
linear OOA(3⁷⁶, 1677720, F₃, 5, 8) (dual of [(1677720, 5), 8388524, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁷⁶, 2097150, F₃, 5, 8) (dual of [(2097150, 5), 10485674, 9]-NRT-code), using
  - OA 4-folding and stacking [i] based on linear OA(3⁷⁶, 8388600, F₃, 8) (dual of [8388600, 8388524, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
linear OOA(3¹⁶⁶, 1677720, F₃, 5, 17) (dual of [(1677720, 5), 8388434, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁶⁶, 8388600, F₃, 17) (dual of [8388600, 8388434, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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.