MinT - Information on Result #1119482

Information on Result #1119482

Linear OOA(3¹⁰⁹, 4194421, F₃, 5, 8) (dual of [(4194421, 5), 20971996, 9]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁵, 121, F₃, 5, 2) (dual of [(121, 5), 600, 3]-NRT-code), using
- appending 3 arbitrary columns [i] based on 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]
linear OOA(3²⁸, 2097150, F₃, 5, 4) (dual of [(2097150, 5), 10485722, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁸, 2391484, F₃, 5, 4) (dual of [(2391484, 5), 11957392, 5]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(3²⁸, 2391485, F₃, 2, 4) (dual of [(2391485, 2), 4782942, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (24, 28, 2391485)-net over F₃, using
      - nets constructed from net-embeddable BCH codes [i]
linear OOA(3⁷⁶, 2097150, F₃, 5, 8) (dual of [(2097150, 5), 10485674, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3⁷⁶, 8388600, F₃, 8) (dual of [8388600, 8388524, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

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