MinT - Information on Result #1235186

Information on Result #1235186

Linear OOA(3¹⁷⁷, 6723842, F₃, 5, 10) (dual of [(6723842, 5), 33619033, 11]-NRT-code), using extracting embedded OOA based on digital (167, 177, 6723842)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (24, 29, 12962)-net over F₃, using
  - net defined by OOA [i] based on linear OOA(3²⁹, 12962, F₃, 5, 5) (dual of [(12962, 5), 64781, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(3²⁹, 25925, F₃, 5) (dual of [25925, 25896, 6]-code), using
      - 1 times code embedding in larger space [i] based on linear OA(3²⁸, 25924, F₃, 5) (dual of [25924, 25896, 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. digital (138, 148, 6710880)-net over F₃, using
  - trace code for nets [i] based on digital (27, 37, 1677720)-net over F₈₁, using
    - net defined by OOA [i] based on linear OOA(81³⁷, 1677720, F₈₁, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
      - OA 5-folding and stacking [i] based on linear OA(81³⁷, 8388600, F₈₁, 10) (dual of [8388600, 8388563, 11]-code), using
        discarding factors / shortening the dual code based on linear OA(81³⁷, large, F₈₁, 10) (dual of [large, large−37, 11]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.