MinT - Information on Result #1010609

Information on Result #1010609

Linear OOA(3¹⁶², 5592558, F₃, 3, 11) (dual of [(5592558, 3), 16777512, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁶, 156, F₃, 3, 5) (dual of [(156, 3), 452, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(3¹⁶, 157, F₃, 2, 5) (dual of [(157, 2), 298, 6]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(3¹, 40, F₃, 2, 1) (dual of [(40, 2), 79, 2]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OOA(3⁴, 40, F₃, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [i]
    3. linear OOA(3¹¹, 77, F₃, 2, 5) (dual of [(77, 2), 143, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (6, 11, 77)-net over F₃, using
        linear code embedding found in a computer search [i]
linear OOA(3¹⁴⁶, 5592402, F₃, 3, 11) (dual of [(5592402, 3), 16777060, 12]-NRT-code), using
- trace code [i] based on linear OOA(9⁷³, 2796201, F₉, 3, 11) (dual of [(2796201, 3), 8388530, 12]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(9⁷³, large, F₉, 11) (dual of [large, large−73, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 9⁸âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.