MinT - Information on Result #1021645

Information on Result #1021645

Linear OOA(5¹⁵⁰, 4194401, F₅, 3, 14) (dual of [(4194401, 3), 12583053, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁸, 100, F₅, 3, 7) (dual of [(100, 3), 282, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(5¹, 25, F₅, 3, 1) (dual of [(25, 3), 74, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(5³, 25, F₅, 3, 2) (dual of [(25, 3), 72, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5³, 31, F₅, 3, 2) (dual of [(31, 3), 90, 3]-NRT-code), using
      - appending 1 arbitrary column [i] based on linear OOA(5³, 31, F₅, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
        appending kth column [i] based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
        Hamming code H(3,5) [i]
  3. linear OOA(5⁴, 25, F₅, 3, 3) (dual of [(25, 3), 71, 4]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
      - ovoid in PG(3,Â 5) [i]
  4. linear OOA(5¹⁰, 25, F₅, 3, 7) (dual of [(25, 3), 65, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 10, 25)-net over F₅, using
      - linear code embedding found in a computer search [i]
linear OOA(5¹³², 4194301, F₅, 3, 14) (dual of [(4194301, 3), 12582771, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(5¹³², 8388602, F₅, 2, 14) (dual of [(8388602, 2), 16777072, 15]-NRT-code), using
  - trace code [i] based on linear OOA(25⁶⁶, 4194301, F₂₅, 2, 14) (dual of [(4194301, 2), 8388536, 15]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁶⁶, 8388602, F₂₅, 14) (dual of [8388602, 8388536, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁶⁶, large, F₂₅, 14) (dual of [large, large−66, 15]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’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.