MinT - Information on Result #1013942

Information on Result #1013942

Linear OOA(7⁷¹, 5623, F₇, 3, 14) (dual of [(5623, 3), 16798, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7¹¹, 21, F₇, 3, 7) (dual of [(21, 3), 52, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7³, 8, F₇, 3, 3) (dual of [(8, 3), 21, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;21,7) [i]
  2. linear OOA(7⁸, 13, F₇, 3, 7) (dual of [(13, 3), 31, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 8, 13)-net over F₇, using
      - 5 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
linear OOA(7⁶⁰, 5602, F₇, 3, 14) (dual of [(5602, 3), 16746, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(7⁶⁰, 16806, F₇, 14) (dual of [16806, 16746, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁶⁰, 16807, F₇, 14) (dual of [16807, 16747, 15]-code), using
    - 1 times truncation [i] based on linear OA(7⁶¹, 16808, F₇, 15) (dual of [16808, 16747, 16]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16808Â | 7¹⁰âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]

Mode: Constructive and linear.

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