MinT - Information on Result #1080923

Information on Result #1080923

Linear OOA(3¹²⁵, 4194352, F₃, 4, 9) (dual of [(4194352, 4), 16777283, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁸, 2391485, F₃, 4, 4) (dual of [(2391485, 4), 9565912, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(3²⁸, 2391485, F₃, 3, 4) (dual of [(2391485, 3), 7174427, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (24, 28, 2391485)-net over F₃, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(3⁹⁷, 2097176, F₃, 4, 9) (dual of [(2097176, 4), 8388607, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁷, 26, F₃, 4, 4) (dual of [(26, 4), 97, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁷, 26, F₃, 3, 4) (dual of [(26, 3), 71, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (3, 7, 26)-net over F₃, using
        nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(3⁹⁰, 2097150, F₃, 4, 9) (dual of [(2097150, 4), 8388510, 10]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(3⁹⁰, 8388600, F₃, 9) (dual of [8388600, 8388510, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁹⁰, large, F₃, 9) (dual of [large, large−90, 10]-code), using
        the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Mode: Constructive and linear.

None.

None.