MinT - Information on Result #1119335

Information on Result #1119335

Linear OOA(3¹⁸⁹, 3355481, F₃, 5, 13) (dual of [(3355481, 5), 16777216, 14]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁸, 41, F₃, 5, 4) (dual of [(41, 5), 197, 5]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(3⁸, 41, F₃, 4, 4) (dual of [(41, 4), 156, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(3⁸, 41, F₃, 3, 4) (dual of [(41, 3), 115, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 8, 41)-net over F₃, using
      - nets constructed from net-embeddable BCH codes [i]
linear OOA(3⁶⁰, 1677720, F₃, 5, 6) (dual of [(1677720, 5), 8388540, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁶⁰, 2796201, F₃, 5, 6) (dual of [(2796201, 5), 13980945, 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(3¹²¹, 1677720, F₃, 5, 13) (dual of [(1677720, 5), 8388479, 14]-NRT-code), using
- OOA 5-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.

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.