MinT - Information on Result #1021305

Information on Result #1021305

Linear OOA(4¹⁴⁰, 2796272, F₄, 3, 14) (dual of [(2796272, 3), 8388676, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹⁹, 71, F₄, 3, 7) (dual of [(71, 3), 194, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹, 17, F₄, 3, 1) (dual of [(17, 3), 50, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹, s, F₄, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [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, 17, F₄, 3, 2) (dual of [(17, 3), 48, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4³, 21, F₄, 3, 2) (dual of [(21, 3), 60, 3]-NRT-code), using
      - appending 1 arbitrary column [i] 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(4⁴, 17, F₄, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(4⁴, 17, F₄, 2, 3) (dual of [(17, 2), 30, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
        ovoid in PG(3,Â 4) [i]
  4. linear OOA(4¹¹, 20, F₄, 3, 7) (dual of [(20, 3), 49, 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(4¹²¹, 2796201, F₄, 3, 14) (dual of [(2796201, 3), 8388482, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4¹²¹, large, F₄, 14) (dual of [large, large−121, 15]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.