MinT - Information on Result #910980

Information on Result #910980

Linear OOA(2⁷⁴, 42, F₂, 2, 39) (dual of [(42, 2), 10, 40]-NRT-code), using concatenation of two NRT-codes based on

linear OA(4⁹, 14, F₄, 7) (dual of [14, 5, 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]
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.

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