MinT - Information on Result #1205414

Information on Result #1205414

Digital (87, 98, 2306864)-net over F₇, using trace code for nets based on digital (38, 49, 1153432)-net over F₄₉, using

net defined by OOA [i] based on linear OOA(49⁴⁹, 1153432, F₄₉, 11, 11) (dual of [(1153432, 11), 12687703, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(49⁴⁹, 5767161, F₄₉, 11) (dual of [5767161, 5767112, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(49⁴⁹, 5767164, F₄₉, 11) (dual of [5767164, 5767115, 12]-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 6]-code), using
        a code by Danev and Olsson [i]
      2. linear OA(49⁴², 5764811, F₄₉, 11) (dual of [5764811, 5764769, 12]-code), using
        constructionÂ X applied to C([0,5]) âŠ‚ C([0,4]) [i] based on
        linear OA(49⁴¹, 5764802, F₄₉, 11) (dual of [5764802, 5764761, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802Â | 49⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
        linear OA(49³³, 5764802, F₄₉, 9) (dual of [5764802, 5764769, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802Â | 49⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
        linear OA(49¹, 9, F₄₉, 1) (dual of [9, 8, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.