MinT - Information on Result #1235219

Information on Result #1235219

Linear OOA(3¹⁹¹, 6717361, F₃, 5, 11) (dual of [(6717361, 5), 33586614, 12]-NRT-code), using extracting embedded OOA based on digital (180, 191, 6717361)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (22, 27, 6481)-net over F₃, using
  - net defined by OOA [i] based on linear OOA(3²⁷, 6481, F₃, 5, 5) (dual of [(6481, 5), 32378, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(3²⁷, 12963, F₃, 5) (dual of [12963, 12936, 6]-code), using
      - 1 times code embedding in larger space [i] based on linear OA(3²⁶, 12962, F₃, 5) (dual of [12962, 12936, 6]-code), using
        trace code [i] based on linear OA(9¹³, 6481, F₉, 5) (dual of [6481, 6468, 6]-code), using
        base reduction for projective spaces (embedding PG(6,81) in PG(12,9)) [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
2. digital (153, 164, 6710880)-net over F₃, using
  - trace code for nets [i] based on digital (30, 41, 1677720)-net over F₈₁, using
    - net defined by OOA [i] based on linear OOA(81⁴¹, 1677720, F₈₁, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
      - OOA 5-folding and stacking with additional row [i] based on linear OA(81⁴¹, 8388601, F₈₁, 11) (dual of [8388601, 8388560, 12]-code), using
        discarding factors / shortening the dual code 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.

Other Results with Identical Parameters

None.

Depending Results

None.