MinT - Information on Result #1117834

Information on Result #1117834

Linear OOA(3²⁴⁶, 1692489, F₃, 5, 19) (dual of [(1692489, 5), 8462199, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁵, 14769, F₃, 5, 9) (dual of [(14769, 5), 73780, 10]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(3⁶⁵, 14770, F₃, 4, 9) (dual of [(14770, 4), 59015, 10]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3⁵, 8, F₃, 4, 4) (dual of [(8, 4), 27, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁵, 8, F₃, 3, 4) (dual of [(8, 3), 19, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (1, 5, 8)-net over F₃, using
        nets constructed from net-embeddable BCH codes [i]
    2. linear OOA(3⁶⁰, 14762, F₃, 4, 9) (dual of [(14762, 4), 58988, 10]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(3⁶⁰, 59048, F₃, 9) (dual of [59048, 58988, 10]-code), using
        the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
linear OOA(3¹⁸¹, 1677720, F₃, 5, 19) (dual of [(1677720, 5), 8388419, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁸¹, 8388600, F₃, 19) (dual of [8388600, 8388419, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.