MinT - Information on Result #1117432

Information on Result #1117432

Linear OOA(3¹⁹¹, 3355478, F₃, 5, 13) (dual of [(3355478, 5), 16777199, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁰, 2796201, F₃, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3⁶⁰, large, F₃, 6) (dual of [large, large−60, 7]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(3¹³¹, 1677739, F₃, 5, 13) (dual of [(1677739, 5), 8388564, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁰, 19, F₃, 5, 6) (dual of [(19, 5), 85, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 10, 19)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹²¹, 1677720, F₃, 5, 13) (dual of [(1677720, 5), 8388479, 14]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(3¹²¹, 8388600, F₃, 13) (dual of [8388600, 8388479, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

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