MinT - Information on Result #1081096

Information on Result #1081096

Linear OOA(3¹⁸⁹, 4194318, F₃, 4, 13) (dual of [(4194318, 4), 16777083, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁰, 2796201, F₃, 4, 6) (dual of [(2796201, 4), 11184744, 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(3¹²⁹, 2097159, F₃, 4, 13) (dual of [(2097159, 4), 8388507, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁸, 9, F₃, 4, 6) (dual of [(9, 4), 28, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (2, 8, 9)-net over F₃, using
      - 1 times m-reduction [i] based on digital (2, 9, 9)-net over F₃, using
        a shift-net [i]
  2. linear OOA(3¹²¹, 2097150, F₃, 4, 13) (dual of [(2097150, 4), 8388479, 14]-NRT-code), using
    - OOA 4-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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