MinT - Information on Result #2639524

Information on Result #2639524

Linear OOA(5⁶⁸, large, F₅, 3, 4), using strength reduction based on linear OOA(5⁶⁸, large, F₅, 3, 6), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(5¹, 2441406, F₅, 3, 1) (dual of [(2441406, 3), 7324217, 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(5¹, 2441406, F₅, 3, 1) (dual of [(2441406, 3), 7324217, 2]-NRT-code) (see above)
3. linear OOA(5¹⁰, 2441406, F₅, 3, 2) (dual of [(2441406, 3), 7324208, 3]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(5¹⁰, 2441406, F₅, 2, 2) (dual of [(2441406, 2), 4882802, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(5¹⁰, 2441406, F₅, 2) (dual of [2441406, 2441396, 3]-code), using
      - Hamming code H(10,5) [i]
4. linear OOA(5¹⁵, 2796201, F₅, 3, 3) (dual of [(2796201, 3), 8388588, 4]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5¹⁵, 3050325, F₅, 3, 3) (dual of [(3050325, 3), 9150960, 4]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OA(5¹⁵, 3050326, F₅, 3) (dual of [3050326, 3050311, 4]-code or 3050326-cap in PG(14,5)), using
      - product of projective cap with cap in AG(6,Â 5) [i] based on linear OA(5⁹, 4700, F₅, 3) (dual of [4700, 4691, 4]-code or 4700-cap in PG(8,5)), using
        caps completed using a computer search [i]
5. linear OOA(5⁴¹, 2796201, F₅, 3, 6) (dual of [(2796201, 3), 8388562, 7]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(5⁴¹, large, F₅, 6) (dual of [large, large−41, 7]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.