MinT - Information on Result #906400

Information on Result #906400

Linear OOA(4¹⁵³, 4194381, F₄, 2, 15) (dual of [(4194381, 2), 8388609, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4²⁰, 80, F₄, 2, 7) (dual of [(80, 2), 140, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹, 20, F₄, 2, 1) (dual of [(20, 2), 39, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹, s, F₄, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(4³, 20, F₄, 2, 2) (dual of [(20, 2), 37, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4³, 21, F₄, 2, 2) (dual of [(21, 2), 39, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(4³, 21, F₄, 2) (dual of [21, 18, 3]-code), using
        Hamming code H(3,4) [i]
  3. linear OOA(4⁵, 20, F₄, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4⁵, 41, F₄, 2, 3) (dual of [(41, 2), 77, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [i]
  4. linear OOA(4¹¹, 20, F₄, 2, 7) (dual of [(20, 2), 29, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 11, 20)-net over F₄, using
      - linear code embedding found in a computer search [i]
linear OOA(4¹³³, 4194301, F₄, 2, 15) (dual of [(4194301, 2), 8388469, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹³³, 8388602, F₄, 15) (dual of [8388602, 8388469, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹³³, large, F₄, 15) (dual of [large, large−133, 16]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.