MinT - Information on Result #1117639

Information on Result #1117639

Linear OOA(3²⁴⁷, 4194355, F₃, 5, 15) (dual of [(4194355, 5), 20971528, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁹, 54, F₃, 5, 7) (dual of [(54, 5), 251, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 20, F₃, 5, 3) (dual of [(20, 5), 95, 4]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
        doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
        ovoid in PG(3,Â 3) [i]
  2. linear OOA(3¹⁴, 34, F₃, 5, 7) (dual of [(34, 5), 156, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 34)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3²²⁸, 4194301, F₃, 5, 15) (dual of [(4194301, 5), 20971277, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3²²⁸, 8388602, F₃, 3, 15) (dual of [(8388602, 3), 25165578, 16]-NRT-code), using
  - trace code [i] based on linear OOA(9¹¹⁴, 4194301, F₉, 3, 15) (dual of [(4194301, 3), 12582789, 16]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(9¹¹⁴, 8388602, F₉, 2, 15) (dual of [(8388602, 2), 16777090, 16]-NRT-code), using
      - trace code [i] based on linear OOA(81⁵⁷, 4194301, F₈₁, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁵⁷, 8388602, F₈₁, 15) (dual of [8388602, 8388545, 16]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁵⁷, large, F₈₁, 15) (dual of [large, large−57, 16]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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.