MinT - Information on Result #821002

Information on Result #821002

Linear OOA(3¹³⁴, 69, F₃, 2, 90) (dual of [(69, 2), 4, 91]-NRT-code), using OOA 2-folding based on linear OA(3¹³⁴, 138, F₃, 90) (dual of [138, 4, 91]-code), using

discarding factors / shortening the dual code based on linear OA(3¹³⁴, 139, F₃, 90) (dual of [139, 5, 91]-code), using
- juxtaposition [i] based on
  1. linear OA(3¹³, 18, F₃, 9) (dual of [18, 5, 10]-code), using
    - 2 times truncation [i] based on linear OA(3¹⁵, 20, F₃, 11) (dual of [20, 5, 12]-code), using
      - residual code [i] based on linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
        dual code (with bound on d by constructionÂ Y1) [i] based on
        linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
        nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
        20 is the largest size of a cap in PG(4,Â 3) [i]
  2. linear OA(3¹¹⁶, 121, F₃, 80) (dual of [121, 5, 81]-code), using
    - Simplex code S(5,3) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 121Â | 3⁵âˆ’1, defining interval IÂ =Â [0,75], and minimum distance dÂ â‰¥ |{5,15,25,…,−52}|+1Â =Â 81 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.