MinT - Information on Result #1081184

Information on Result #1081184

Linear OOA(3¹⁷⁰, 2097218, F₃, 4, 15) (dual of [(2097218, 4), 8388702, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁰, 68, F₃, 4, 7) (dual of [(68, 4), 252, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁶, 56, F₃, 4, 3) (dual of [(56, 4), 218, 4]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(3⁶, 56, F₃, 3, 3) (dual of [(56, 3), 162, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁶, 56, F₃, 2, 3) (dual of [(56, 2), 106, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
  2. linear OOA(3¹⁴, 34, F₃, 4, 7) (dual of [(34, 4), 122, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 34)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹⁵⁰, 2097150, F₃, 4, 15) (dual of [(2097150, 4), 8388450, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹⁵⁰, 8388600, F₃, 15) (dual of [8388600, 8388450, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

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