MinT - Information on Result #1021192

Information on Result #1021192

Linear OOA(3¹²³, 2796432, F₃, 3, 11) (dual of [(2796432, 3), 8389173, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁷, 231, F₃, 3, 5) (dual of [(231, 3), 676, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹, 77, F₃, 3, 1) (dual of [(77, 3), 230, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(3⁵, 77, F₃, 3, 2) (dual of [(77, 3), 226, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁵, 121, F₃, 3, 2) (dual of [(121, 3), 358, 3]-NRT-code), using
      - appending 1 arbitrary column [i] based on linear OOA(3⁵, 121, F₃, 2, 2) (dual of [(121, 2), 237, 3]-NRT-code), using
        appending kth column [i] based on linear OA(3⁵, 121, F₃, 2) (dual of [121, 116, 3]-code), using
        Hamming code H(5,3) [i]
  3. linear OOA(3¹¹, 77, F₃, 3, 5) (dual of [(77, 3), 220, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 11, 77)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹⁰⁶, 2796201, F₃, 3, 11) (dual of [(2796201, 3), 8388497, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁰⁶, large, F₃, 11) (dual of [large, large−106, 12]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.