MinT - Information on Result #1010431

Information on Result #1010431

Linear OOA(3⁸⁵, 5592422, F₃, 3, 7) (dual of [(5592422, 3), 16777181, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁰, 3713024, F₃, 3, 3) (dual of [(3713024, 3), 11139052, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(3²⁰, 3713024, F₃, 2, 3) (dual of [(3713024, 2), 7426028, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3²⁰, 3713024, F₃, 3) (dual of [3713024, 3713004, 4]-code or 3713024-cap in PG(19,3)), using
    - large caps in PG(u,Â 3) [i]
linear OOA(3⁶⁵, 2796211, F₃, 3, 7) (dual of [(2796211, 3), 8388568, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁴, 10, F₃, 3, 3) (dual of [(10, 3), 26, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁴, 10, F₃, 2, 3) (dual of [(10, 2), 16, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
        ovoid in PG(3,Â 3) [i]
  2. linear OOA(3⁶¹, 2796201, F₃, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]

Mode: Constructive and linear.

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