MinT - Information on Result #670292

Information on Result #670292

Linear OA(81⁶⁷, 6725, F₈₁, 25) (dual of [6725, 6658, 26]-code), using (u,Â u+v)-construction based on

linear OA(81¹⁸, 163, F₈₁, 12) (dual of [163, 145, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(81¹⁸, 164, F₈₁, 12) (dual of [164, 146, 13]-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OA(81⁶, 82, F₈₁, 6) (dual of [82, 76, 7]-code or 82-arc in PG(5,81)), using
      - extended Reedâ€“Solomon code RS_e(76,81) [i]
    2. linear OA(81¹², 82, F₈₁, 12) (dual of [82, 70, 13]-code or 82-arc in PG(11,81)), using
      - extended Reedâ€“Solomon code RS_e(70,81) [i]
linear OA(81⁴⁹, 6562, F₈₁, 25) (dual of [6562, 6513, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

Mode: Constructive and linear.

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