MinT - Information on Result #1117804

Information on Result #1117804

Linear OOA(3²⁰⁰, 1677746, F₃, 5, 19) (dual of [(1677746, 5), 8388530, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁹, 26, F₃, 5, 9) (dual of [(26, 5), 111, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁶, 14, F₃, 5, 4) (dual of [(14, 5), 64, 5]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(3⁶, 14, F₃, 4, 4) (dual of [(14, 4), 50, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁶, 14, F₃, 3, 4) (dual of [(14, 3), 36, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (2, 6, 14)-net over F₃, using
        linear code embedding found in a computer search [i]
  2. linear OOA(3¹³, 13, F₃, 5, 9) (dual of [(13, 5), 52, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 13, 13)-net over F₃, using
      - a shift-net [i]
linear OOA(3¹⁸¹, 1677720, F₃, 5, 19) (dual of [(1677720, 5), 8388419, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁸¹, 8388600, F₃, 19) (dual of [8388600, 8388419, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Constructive and linear.

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