MinT - Information on Result #1081310

Information on Result #1081310

Linear OOA(3¹⁹⁹, 2097176, F₃, 4, 18) (dual of [(2097176, 4), 8388505, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁹, 26, F₃, 4, 9) (dual of [(26, 4), 85, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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, 4, 9) (dual of [(13, 4), 39, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 13, 13)-net over F₃, using
      - a shift-net [i]
linear OOA(3¹⁸⁰, 2097150, F₃, 4, 18) (dual of [(2097150, 4), 8388420, 19]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹⁸⁰, 8388600, F₃, 18) (dual of [8388600, 8388420, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and linear.

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