MinT - Information on Result #1117657

Information on Result #1117657

Linear OOA(3¹⁷², 1677764, F₃, 5, 16) (dual of [(1677764, 5), 8388648, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²¹, 44, F₃, 5, 8) (dual of [(44, 5), 199, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁷, 26, F₃, 5, 4) (dual of [(26, 5), 123, 5]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(3⁷, 26, F₃, 4, 4) (dual of [(26, 4), 97, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁷, 26, F₃, 3, 4) (dual of [(26, 3), 71, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (3, 7, 26)-net over F₃, using
        nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(3¹⁴, 22, F₃, 5, 8) (dual of [(22, 5), 96, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 14, 22)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹⁵¹, 1677720, F₃, 5, 16) (dual of [(1677720, 5), 8388449, 17]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁵¹, 8388600, F₃, 16) (dual of [8388600, 8388449, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

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