MinT - Information on Result #662530

Information on Result #662530

Linear OA(4²⁴, 32, F₄, 15) (dual of [32, 8, 16]-code), using (u,Â u+v)-construction based on

linear OA(4⁹, 16, F₄, 7) (dual of [16, 7, 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 OA(4¹⁵, 16, F₄, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
- dual of repetition code with length 16 [i]

Mode: Constructive and linear.

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