MinT - Information on Result #2417344

Information on Result #2417344

Linear OOA(2⁷⁰, 39, F₂, 2, 38) (dual of [(39, 2), 8, 39]-NRT-code), using strength reduction based on linear OOA(2⁷⁰, 39, F₂, 2, 39) (dual of [(39, 2), 8, 40]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(4⁹, 13, F₄, 7) (dual of [13, 4, 8]-code), using
  - discarding factors / shortening the dual code based on 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 OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [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.