MinT - Information on Result #805907

Information on Result #805907

Linear OOA(2³⁵, 25, F₂, 2, 15) (dual of [(25, 2), 15, 16]-NRT-code), using OOA 2-folding based on linear OA(2³⁵, 50, F₂, 15) (dual of [50, 15, 16]-code), using

discarding factors / shortening the dual code based on linear OA(2³⁵, 51, F₂, 15) (dual of [51, 16, 16]-code), using
- concatenation of two codes [i] based on
  1. linear OA(4⁹, 17, F₄, 7) (dual of [17, 8, 8]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(4⁸, 17, F₄, 6) (dual of [17, 9, 7]-code), using
        the BCH-code C(I) with length 17Â | 4⁴âˆ’1, defining interval IÂ =Â {1,4,7,…,16}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. nonexistence of linear OA(4⁷, 10, F₄, 6) (dual of [10, 3, 7]-code), because
        bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
  2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 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, 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.