MinT - Information on Result #1084719

Information on Result #1084719

Linear OOA(3⁸³, 5592415, F₃, 4, 6) (dual of [(5592415, 4), 22369577, 7]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3³, 13, F₃, 4, 2) (dual of [(13, 4), 49, 3]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(3³, 13, F₃, 2, 2) (dual of [(13, 2), 23, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
    - Hamming code H(3,3) [i]
linear OOA(3²⁰, 2796201, F₃, 4, 3) (dual of [(2796201, 4), 11184784, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁰, 3713024, F₃, 4, 3) (dual of [(3713024, 4), 14852076, 4]-NRT-code), using
  - appending 1 arbitrary column [i] 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(3⁶⁰, 2796201, F₃, 4, 6) (dual of [(2796201, 4), 11184744, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3⁶⁰, large, F₃, 6) (dual of [large, large−60, 7]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

Mode: Constructive and linear.

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