MinT - Information on Result #1193492

Information on Result #1193492

Digital (94, 105, 2825365)-net over F₉, using net defined by OOA based on linear OOA(9¹⁰⁵, 2825365, F₉, 15, 11) (dual of [(2825365, 15), 42380370, 12]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(9¹⁰⁵, 5650731, F₉, 3, 11) (dual of [(5650731, 3), 16952088, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9²³, 58329, F₉, 3, 5) (dual of [(58329, 3), 174964, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(9⁰, 6481, F₉, 3, 0) (dual of [(6481, 3), 19443, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9⁰, s, F₉, 3, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(9⁰, 6481, F₉, 3, 0) (dual of [(6481, 3), 19443, 1]-NRT-code) (see above)
      3. linear OOA(9⁰, 6481, F₉, 3, 0) (dual of [(6481, 3), 19443, 1]-NRT-code) (see above)
      4. linear OOA(9⁰, 6481, F₉, 3, 0) (dual of [(6481, 3), 19443, 1]-NRT-code) (see above)
      5. linear OOA(9¹, 6481, F₉, 3, 1) (dual of [(6481, 3), 19442, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9¹, s, F₉, 3, 1) for arbitrarily large s, using
        appending 2 arbitrary columns [i] based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      6. linear OOA(9¹, 6481, F₉, 3, 1) (dual of [(6481, 3), 19442, 2]-NRT-code) (see above)
      7. linear OOA(9¹, 6481, F₉, 3, 1) (dual of [(6481, 3), 19442, 2]-NRT-code) (see above)
      8. linear OOA(9⁵, 6481, F₉, 3, 2) (dual of [(6481, 3), 19438, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9⁵, 7381, F₉, 3, 2) (dual of [(7381, 3), 22138, 3]-NRT-code), using
        appending 1 arbitrary column [i] based on linear OOA(9⁵, 7381, F₉, 2, 2) (dual of [(7381, 2), 14757, 3]-NRT-code), using
        appending kth column [i] based on linear OA(9⁵, 7381, F₉, 2) (dual of [7381, 7376, 3]-code), using
        Hamming code H(5,9) [i]
      9. linear OOA(9¹⁵, 6481, F₉, 3, 5) (dual of [(6481, 3), 19428, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(9¹⁵, 12963, F₉, 5) (dual of [12963, 12948, 6]-code), using
        1 times code embedding in larger space [i] based on linear OA(9¹⁴, 12962, F₉, 5) (dual of [12962, 12948, 6]-code), using
        trace code [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
  2. linear OOA(9⁸², 5592402, F₉, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
    - trace code [i] based on linear OOA(81⁴¹, 2796201, F₈₁, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.