MinT - Information on Result #1081257

Information on Result #1081257

Linear OOA(3²³⁹, 4194314, F₃, 4, 16) (dual of [(4194314, 4), 16777017, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁷⁶, 2097150, F₃, 4, 8) (dual of [(2097150, 4), 8388524, 9]-NRT-code), using
- OOA 4-folding [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]
linear OOA(3¹⁶³, 2097164, F₃, 4, 16) (dual of [(2097164, 4), 8388493, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹², 14, F₃, 4, 8) (dual of [(14, 4), 44, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 12, 14)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹⁵¹, 2097150, F₃, 4, 16) (dual of [(2097150, 4), 8388449, 17]-NRT-code), using
    - OOA 4-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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