MinT - Information on Result #1021150

Information on Result #1021150

Linear OOA(3¹²⁴, 5592422, F₃, 3, 9) (dual of [(5592422, 3), 16777142, 10]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
    - doubling the cap [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]
linear OOA(3²⁹, 2796201, F₃, 3, 4) (dual of [(2796201, 3), 8388574, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁹, 4782967, F₃, 3, 4) (dual of [(4782967, 3), 14348872, 5]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(3²⁹, 4782968, F₃, 2, 4) (dual of [(4782968, 2), 9565907, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (25, 29, 4782968)-net over F₃, using
      - nets constructed from net-embeddable BCH codes [i]
linear OOA(3⁹⁰, 2796201, F₃, 3, 9) (dual of [(2796201, 3), 8388513, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3⁹⁰, large, F₃, 9) (dual of [large, large−90, 10]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Mode: Constructive and linear.

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