MinT - Information on Result #894985

Information on Result #894985

Linear OOA(3¹⁰⁹, 4194507, F₃, 2, 10) (dual of [(4194507, 2), 8388905, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁸, 206, F₃, 2, 5) (dual of [(206, 2), 394, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 121, F₃, 2, 2) (dual of [(121, 2), 237, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(3⁵, 121, F₃, 2) (dual of [121, 116, 3]-code), using
      - Hamming code H(5,3) [i]
  2. linear OOA(3¹³, 103, F₃, 2, 5) (dual of [(103, 2), 193, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (8, 13, 103)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3⁹¹, 4194301, F₃, 2, 10) (dual of [(4194301, 2), 8388511, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁹¹, 8388602, F₃, 10) (dual of [8388602, 8388511, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁹¹, large, F₃, 10) (dual of [large, large−91, 11]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

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